Fundamental Solutions to Pell's Equation for $n = 1001 \mathinner{\ldotp\ldotp} 2000$


The fundamental solutions to Pell's equation (also known as "minimal solutions") presented below were computed in 2012 using a Python program that implements the chakravala method (attributed to Bhaskara II). $N$ is skipped if it is not square-free (i.e., if it is a perfect square or a multiple of a square).

$N$ $x$ $y$ Fundamental Solution
$1001$ $1060905$ $33532$ $1060905^{2} \, - \, $$1001$$ \, \cdot \, 33532^{2} = 1$
$1002$ $206869247$ $6535248$ $206869247^{2} \, - \, $$1002$$ \, \cdot \, 6535248^{2} = 1$
$1003$ $9026$ $285$ $9026^{2} \, - \, $$1003$$ \, \cdot \, 285^{2} = 1$
$1005$ $2950149761$ $93059568$ $2950149761^{2} \, - \, $$1005$$ \, \cdot \, 93059568^{2} = 1$
$1006$ $14125267563780214605455$ $445346140255574921748$ $14125267563780214605455^{2} \, - \, $$1006$$ \, \cdot \, 445346140255574921748^{2} = 1$
$1007$ $476$ $15$ $476^{2} \, - \, $$1007$$ \, \cdot \, 15^{2} = 1$
$1009$ $583201$ $18360$ $583201^{2} \, - \, $$1009$$ \, \cdot \, 18360^{2} = 1$
$1010$ $3395619$ $106846$ $3395619^{2} \, - \, $$1010$$ \, \cdot \, 106846^{2} = 1$
$1011$ $8426$ $265$ $8426^{2} \, - \, $$1011$$ \, \cdot \, 265^{2} = 1$
$1013$ $309159979019115849$ $9713562669309460$ $309159979019115849^{2} \, - \, $$1013$$ \, \cdot \, 9713562669309460^{2} = 1$
$1015$ $352871$ $11076$ $352871^{2} \, - \, $$1015$$ \, \cdot \, 11076^{2} = 1$
$1018$ $15155578752298003$ $475005498176334$ $15155578752298003^{2} \, - \, $$1018$$ \, \cdot \, 475005498176334^{2} = 1$
$1019$ $6089923321730$ $190776436539$ $6089923321730^{2} \, - \, $$1019$$ \, \cdot \, 190776436539^{2} = 1$
$1021$ $198723867690977573219668252231077415636351801801$ $6219237759214762827187409503019432615976684540$ $198723867690977573219668252231077415636351801801^{2} \, - \, $$1021$$ \, \cdot \, 6219237759214762827187409503019432615976684540^{2} = 1$
$1022$ $1023$ $32$ $1023^{2} \, - \, $$1022$$ \, \cdot \, 32^{2} = 1$
$1023$ $32$ $1$ $32^{2} \, - \, $$1023$$ \, \cdot \, 1^{2} = 1$
$1027$ $133150393$ $4154868$ $133150393^{2} \, - \, $$1027$$ \, \cdot \, 4154868^{2} = 1$
$1030$ $884307011291$ $27553987434$ $884307011291^{2} \, - \, $$1030$$ \, \cdot \, 27553987434^{2} = 1$
$1031$ $651737448664200$ $20297537082877$ $651737448664200^{2} \, - \, $$1031$$ \, \cdot \, 20297537082877^{2} = 1$
$1033$ $69833593956354694952807071952492833$ $2172772383489805842331071281808456$ $69833593956354694952807071952492833^{2} \, - \, $$1033$$ \, \cdot \, 2172772383489805842331071281808456^{2} = 1$
$1034$ $15885$ $494$ $15885^{2} \, - \, $$1034$$ \, \cdot \, 494^{2} = 1$
$1037$ $8710152963849$ $270480776020$ $8710152963849^{2} \, - \, $$1037$$ \, \cdot \, 270480776020^{2} = 1$
$1038$ $15404267$ $478126$ $15404267^{2} \, - \, $$1038$$ \, \cdot \, 478126^{2} = 1$
$1039$ $493194634979076339348637520$ $15300674275156671864306921$ $493194634979076339348637520^{2} \, - \, $$1039$$ \, \cdot \, 15300674275156671864306921^{2} = 1$
$1041$ $770918649927575$ $23893687943492$ $770918649927575^{2} \, - \, $$1041$$ \, \cdot \, 23893687943492^{2} = 1$
$1042$ $1302499$ $40350$ $1302499^{2} \, - \, $$1042$$ \, \cdot \, 40350^{2} = 1$
$1043$ $576927$ $17864$ $576927^{2} \, - \, $$1043$$ \, \cdot \, 17864^{2} = 1$
$1045$ $456191$ $14112$ $456191^{2} \, - \, $$1045$$ \, \cdot \, 14112^{2} = 1$
$1046$ $3987042510565$ $123277842162$ $3987042510565^{2} \, - \, $$1046$$ \, \cdot \, 123277842162^{2} = 1$
$1047$ $136807$ $4228$ $136807^{2} \, - \, $$1047$$ \, \cdot \, 4228^{2} = 1$
$1049$ $4720747718766511296768801$ $145754861076386671221320$ $4720747718766511296768801^{2} \, - \, $$1049$$ \, \cdot \, 145754861076386671221320^{2} = 1$
$1051$ $955382766460015065912973250$ $29469722410666558657086507$ $955382766460015065912973250^{2} \, - \, $$1051$$ \, \cdot \, 29469722410666558657086507^{2} = 1$
$1054$ $3355576256056895$ $103358645005416$ $3355576256056895^{2} \, - \, $$1054$$ \, \cdot \, 103358645005416^{2} = 1$
$1055$ $1689$ $52$ $1689^{2} \, - \, $$1055$$ \, \cdot \, 52^{2} = 1$
$1057$ $239637339568529407$ $7370840200132992$ $239637339568529407^{2} \, - \, $$1057$$ \, \cdot \, 7370840200132992^{2} = 1$
$1059$ $5983486610$ $183868081$ $5983486610^{2} \, - \, $$1059$$ \, \cdot \, 183868081^{2} = 1$
$1061$ $170800615664635332564330517881801$ $5243626382156167474921782674260$ $170800615664635332564330517881801^{2} \, - \, $$1061$$ \, \cdot \, 5243626382156167474921782674260^{2} = 1$
$1063$ $1745324831097224$ $53531527412685$ $1745324831097224^{2} \, - \, $$1063$$ \, \cdot \, 53531527412685^{2} = 1$
$1065$ $82667999$ $2533160$ $82667999^{2} \, - \, $$1065$$ \, \cdot \, 2533160^{2} = 1$
$1066$ $23597172197299$ $722738781870$ $23597172197299^{2} \, - \, $$1066$$ \, \cdot \, 722738781870^{2} = 1$
$1067$ $98$ $3$ $98^{2} \, - \, $$1067$$ \, \cdot \, 3^{2} = 1$
$1069$ $742925865816843150858935268959512942700219559049$ $22722526912283010072320240710785462723519145740$ $742925865816843150858935268959512942700219559049^{2} \, - \, $$1069$$ \, \cdot \, 22722526912283010072320240710785462723519145740^{2} = 1$
$1070$ $2948491$ $90138$ $2948491^{2} \, - \, $$1070$$ \, \cdot \, 90138^{2} = 1$
$1073$ $4116510849$ $125669360$ $4116510849^{2} \, - \, $$1073$$ \, \cdot \, 125669360^{2} = 1$
$1074$ $3489425$ $106476$ $3489425^{2} \, - \, $$1074$$ \, \cdot \, 106476^{2} = 1$
$1077$ $23522399$ $716760$ $23522399^{2} \, - \, $$1077$$ \, \cdot \, 716760^{2} = 1$
$1079$ $180576876$ $5497325$ $180576876^{2} \, - \, $$1079$$ \, \cdot \, 5497325^{2} = 1$
$1081$ $293215056101715119615$ $8918122218728007648$ $293215056101715119615^{2} \, - \, $$1081$$ \, \cdot \, 8918122218728007648^{2} = 1$
$1082$ $3185797868403$ $96851106538$ $3185797868403^{2} \, - \, $$1082$$ \, \cdot \, 96851106538^{2} = 1$
$1085$ $17919$ $544$ $17919^{2} \, - \, $$1085$$ \, \cdot \, 544^{2} = 1$
$1086$ $725$ $22$ $725^{2} \, - \, $$1086$$ \, \cdot \, 22^{2} = 1$
$1087$ $1088$ $33$ $1088^{2} \, - \, $$1087$$ \, \cdot \, 33^{2} = 1$
$1090$ $2179$ $66$ $2179^{2} \, - \, $$1090$$ \, \cdot \, 66^{2} = 1$
$1091$ $1090$ $33$ $1090^{2} \, - \, $$1091$$ \, \cdot \, 33^{2} = 1$
$1093$ $649296649$ $19639620$ $649296649^{2} \, - \, $$1093$$ \, \cdot \, 19639620^{2} = 1$
$1094$ $14898540581538085$ $450438047467914$ $14898540581538085^{2} \, - \, $$1094$$ \, \cdot \, 450438047467914^{2} = 1$
$1095$ $364$ $11$ $364^{2} \, - \, $$1095$$ \, \cdot \, 11^{2} = 1$
$1097$ $883619927128353$ $26678547908792$ $883619927128353^{2} \, - \, $$1097$$ \, \cdot \, 26678547908792^{2} = 1$
$1099$ $1593163815326$ $48057545715$ $1593163815326^{2} \, - \, $$1099$$ \, \cdot \, 48057545715^{2} = 1$
$1101$ $24313015$ $732732$ $24313015^{2} \, - \, $$1101$$ \, \cdot \, 732732^{2} = 1$
$1102$ $11382443$ $342882$ $11382443^{2} \, - \, $$1102$$ \, \cdot \, 342882^{2} = 1$
$1103$ $2346242745024$ $70645611145$ $2346242745024^{2} \, - \, $$1103$$ \, \cdot \, 70645611145^{2} = 1$
$1105$ $1623132289$ $48828432$ $1623132289^{2} \, - \, $$1105$$ \, \cdot \, 48828432^{2} = 1$
$1106$ $5055$ $152$ $5055^{2} \, - \, $$1106$$ \, \cdot \, 152^{2} = 1$
$1109$ $744702728637239515399291224201$ $22362336179089374248695940740$ $744702728637239515399291224201^{2} \, - \, $$1109$$ \, \cdot \, 22362336179089374248695940740^{2} = 1$
$1110$ $1999$ $60$ $1999^{2} \, - \, $$1110$$ \, \cdot \, 60^{2} = 1$
$1111$ $100$ $3$ $100^{2} \, - \, $$1111$$ \, \cdot \, 3^{2} = 1$
$1113$ $702463$ $21056$ $702463^{2} \, - \, $$1113$$ \, \cdot \, 21056^{2} = 1$
$1114$ $74707907636890165020962560915699$ $2238329289963186402088628832570$ $74707907636890165020962560915699^{2} \, - \, $$1114$$ \, \cdot \, 2238329289963186402088628832570^{2} = 1$
$1115$ $4560126$ $136565$ $4560126^{2} \, - \, $$1115$$ \, \cdot \, 136565^{2} = 1$
$1117$ $87897747594260774254246835664214545379849$ $2629972211566463612149241455626172190220$ $87897747594260774254246835664214545379849^{2} \, - \, $$1117$$ \, \cdot \, 2629972211566463612149241455626172190220^{2} = 1$
$1118$ $4213$ $126$ $4213^{2} \, - \, $$1118$$ \, \cdot \, 126^{2} = 1$
$1119$ $31657255$ $946364$ $31657255^{2} \, - \, $$1119$$ \, \cdot \, 946364^{2} = 1$
$1121$ $151985104364951$ $4539397558620$ $151985104364951^{2} \, - \, $$1121$$ \, \cdot \, 4539397558620^{2} = 1$
$1122$ $67$ $2$ $67^{2} \, - \, $$1122$$ \, \cdot \, 2^{2} = 1$
$1123$ $16506645562632482$ $492571123214799$ $16506645562632482^{2} \, - \, $$1123$$ \, \cdot \, 492571123214799^{2} = 1$
$1126$ $91205$ $2718$ $91205^{2} \, - \, $$1126$$ \, \cdot \, 2718^{2} = 1$
$1129$ $56449$ $1680$ $56449^{2} \, - \, $$1129$$ \, \cdot \, 1680^{2} = 1$
$1130$ $381939$ $11362$ $381939^{2} \, - \, $$1130$$ \, \cdot \, 11362^{2} = 1$
$1131$ $368185$ $10948$ $368185^{2} \, - \, $$1131$$ \, \cdot \, 10948^{2} = 1$
$1133$ $514999$ $15300$ $514999^{2} \, - \, $$1133$$ \, \cdot \, 15300^{2} = 1$
$1135$ $10614754956124$ $315073619505$ $10614754956124^{2} \, - \, $$1135$$ \, \cdot \, 315073619505^{2} = 1$
$1137$ $650468934487$ $19290626292$ $650468934487^{2} \, - \, $$1137$$ \, \cdot \, 19290626292^{2} = 1$
$1138$ $243198723043$ $7209251214$ $243198723043^{2} \, - \, $$1138$$ \, \cdot \, 7209251214^{2} = 1$
$1139$ $135$ $4$ $135^{2} \, - \, $$1139$$ \, \cdot \, 4^{2} = 1$
$1141$ $1036782394157223963237125215$ $30693385322765657197397208$ $1036782394157223963237125215^{2} \, - \, $$1141$$ \, \cdot \, 30693385322765657197397208^{2} = 1$
$1142$ $906612101$ $26828010$ $906612101^{2} \, - \, $$1142$$ \, \cdot \, 26828010^{2} = 1$
$1145$ $3135009$ $92648$ $3135009^{2} \, - \, $$1145$$ \, \cdot \, 92648^{2} = 1$
$1146$ $3447551$ $101840$ $3447551^{2} \, - \, $$1146$$ \, \cdot \, 101840^{2} = 1$
$1147$ $9447152318$ $278945403$ $9447152318^{2} \, - \, $$1147$$ \, \cdot \, 278945403^{2} = 1$
$1149$ $7207295$ $212624$ $7207295^{2} \, - \, $$1149$$ \, \cdot \, 212624^{2} = 1$
$1151$ $65905671840$ $1942607807$ $65905671840^{2} \, - \, $$1151$$ \, \cdot \, 1942607807^{2} = 1$
$1153$ $21002267655460685387089654909788673$ $618516849717028248841100388607776$ $21002267655460685387089654909788673^{2} \, - \, $$1153$$ \, \cdot \, 618516849717028248841100388607776^{2} = 1$
$1154$ $1155$ $34$ $1155^{2} \, - \, $$1154$$ \, \cdot \, 34^{2} = 1$
$1155$ $34$ $1$ $34^{2} \, - \, $$1155$$ \, \cdot \, 1^{2} = 1$
$1157$ $2313$ $68$ $2313^{2} \, - \, $$1157$$ \, \cdot \, 68^{2} = 1$
$1158$ $1157$ $34$ $1157^{2} \, - \, $$1158$$ \, \cdot \, 34^{2} = 1$
$1159$ $1669145551424551$ $49028938575180$ $1669145551424551^{2} \, - \, $$1159$$ \, \cdot \, 49028938575180^{2} = 1$
$1162$ $22616173$ $663462$ $22616173^{2} \, - \, $$1162$$ \, \cdot \, 663462^{2} = 1$
$1163$ $1260321002$ $36956541$ $1260321002^{2} \, - \, $$1163$$ \, \cdot \, 36956541^{2} = 1$
$1165$ $17522747454441842569$ $513380346877228788$ $17522747454441842569^{2} \, - \, $$1165$$ \, \cdot \, 513380346877228788^{2} = 1$
$1166$ $660427701$ $19340870$ $660427701^{2} \, - \, $$1166$$ \, \cdot \, 19340870^{2} = 1$
$1167$ $373828$ $10943$ $373828^{2} \, - \, $$1167$$ \, \cdot \, 10943^{2} = 1$
$1169$ $184235994983935$ $5388491828064$ $184235994983935^{2} \, - \, $$1169$$ \, \cdot \, 5388491828064^{2} = 1$
$1171$ $52268476130$ $1527430263$ $52268476130^{2} \, - \, $$1171$$ \, \cdot \, 1527430263^{2} = 1$
$1173$ $137$ $4$ $137^{2} \, - \, $$1173$$ \, \cdot \, 4^{2} = 1$
$1174$ $4672442879206569303591365$ $136367209121366140674774$ $4672442879206569303591365^{2} \, - \, $$1174$$ \, \cdot \, 136367209121366140674774^{2} = 1$
$1177$ $9482010153904475351$ $276383546065778460$ $9482010153904475351^{2} \, - \, $$1177$$ \, \cdot \, 276383546065778460^{2} = 1$
$1178$ $59583$ $1736$ $59583^{2} \, - \, $$1178$$ \, \cdot \, 1736^{2} = 1$
$1181$ $299819549856198391714823049$ $8724388547388468773672620$ $299819549856198391714823049^{2} \, - \, $$1181$$ \, \cdot \, 8724388547388468773672620^{2} = 1$
$1182$ $27252587$ $792682$ $27252587^{2} \, - \, $$1182$$ \, \cdot \, 792682^{2} = 1$
$1185$ $41418751$ $1203200$ $41418751^{2} \, - \, $$1185$$ \, \cdot \, 1203200^{2} = 1$
$1186$ $6320195$ $183522$ $6320195^{2} \, - \, $$1186$$ \, \cdot \, 183522^{2} = 1$
$1187$ $39095175626$ $1134743775$ $39095175626^{2} \, - \, $$1187$$ \, \cdot \, 1134743775^{2} = 1$
$1189$ $143698819617947177389973449$ $4167372038262395220808020$ $143698819617947177389973449^{2} \, - \, $$1189$$ \, \cdot \, 4167372038262395220808020^{2} = 1$
$1190$ $69$ $2$ $69^{2} \, - \, $$1190$$ \, \cdot \, 2^{2} = 1$
$1191$ $3175$ $92$ $3175^{2} \, - \, $$1191$$ \, \cdot \, 92^{2} = 1$
$1193$ $1462023556679567649$ $42328623757159480$ $1462023556679567649^{2} \, - \, $$1193$$ \, \cdot \, 42328623757159480^{2} = 1$
$1194$ $21647468749$ $626476750$ $21647468749^{2} \, - \, $$1194$$ \, \cdot \, 626476750^{2} = 1$
$1195$ $4650060959$ $134516232$ $4650060959^{2} \, - \, $$1195$$ \, \cdot \, 134516232^{2} = 1$
$1198$ $4206256963502359251599$ $121525492983646316460$ $4206256963502359251599^{2} \, - \, $$1198$$ \, \cdot \, 121525492983646316460^{2} = 1$
$1199$ $497777820$ $14375599$ $497777820^{2} \, - \, $$1199$$ \, \cdot \, 14375599^{2} = 1$
$1201$ $124015777380821763117401108566632174583648616449$ $3578536376412875571438541467679723838177648640$ $124015777380821763117401108566632174583648616449^{2} \, - \, $$1201$$ \, \cdot \, 3578536376412875571438541467679723838177648640^{2} = 1$
$1202$ $10817$ $312$ $10817^{2} \, - \, $$1202$$ \, \cdot \, 312^{2} = 1$
$1203$ $434282$ $12521$ $434282^{2} \, - \, $$1203$$ \, \cdot \, 12521^{2} = 1$
$1205$ $7174089$ $206668$ $7174089^{2} \, - \, $$1205$$ \, \cdot \, 206668^{2} = 1$
$1207$ $1159928$ $33387$ $1159928^{2} \, - \, $$1207$$ \, \cdot \, 33387^{2} = 1$
$1209$ $57029335$ $1640156$ $57029335^{2} \, - \, $$1209$$ \, \cdot \, 1640156^{2} = 1$
$1211$ $174$ $5$ $174^{2} \, - \, $$1211$$ \, \cdot \, 5^{2} = 1$
$1213$ $9968927282677513$ $286231896207756$ $9968927282677513^{2} \, - \, $$1213$$ \, \cdot \, 286231896207756^{2} = 1$
$1214$ $73150798374975$ $2099470260104$ $73150798374975^{2} \, - \, $$1214$$ \, \cdot \, 2099470260104^{2} = 1$
$1217$ $1526641059203073$ $43761444552128$ $1526641059203073^{2} \, - \, $$1217$$ \, \cdot \, 43761444552128^{2} = 1$
$1218$ $349$ $10$ $349^{2} \, - \, $$1218$$ \, \cdot \, 10^{2} = 1$
$1219$ $26811112454855326$ $767914700295135$ $26811112454855326^{2} \, - \, $$1219$$ \, \cdot \, 767914700295135^{2} = 1$
$1221$ $21385$ $612$ $21385^{2} \, - \, $$1221$$ \, \cdot \, 612^{2} = 1$
$1222$ $7734245409307$ $221249524122$ $7734245409307^{2} \, - \, $$1222$$ \, \cdot \, 221249524122^{2} = 1$
$1223$ $1224$ $35$ $1224^{2} \, - \, $$1223$$ \, \cdot \, 35^{2} = 1$
$1226$ $2451$ $70$ $2451^{2} \, - \, $$1226$$ \, \cdot \, 70^{2} = 1$
$1227$ $1226$ $35$ $1226^{2} \, - \, $$1227$$ \, \cdot \, 35^{2} = 1$
$1229$ $923640201$ $26346740$ $923640201^{2} \, - \, $$1229$$ \, \cdot \, 26346740^{2} = 1$
$1230$ $491$ $14$ $491^{2} \, - \, $$1230$$ \, \cdot \, 14^{2} = 1$
$1231$ $2051772574240109813487200$ $58479034523501522751177$ $2051772574240109813487200^{2} \, - \, $$1231$$ \, \cdot \, 58479034523501522751177^{2} = 1$
$1234$ $586327869067265$ $16691023073856$ $586327869067265^{2} \, - \, $$1234$$ \, \cdot \, 16691023073856^{2} = 1$
$1235$ $246$ $7$ $246^{2} \, - \, $$1235$$ \, \cdot \, 7^{2} = 1$
$1237$ $2347849777171254083668416002496336649$ $66755254524262858038831090292970460$ $2347849777171254083668416002496336649^{2} \, - \, $$1237$$ \, \cdot \, 66755254524262858038831090292970460^{2} = 1$
$1238$ $902501$ $25650$ $902501^{2} \, - \, $$1238$$ \, \cdot \, 25650^{2} = 1$
$1239$ $176$ $5$ $176^{2} \, - \, $$1239$$ \, \cdot \, 5^{2} = 1$
$1241$ $2311324401362049$ $65610751710320$ $2311324401362049^{2} \, - \, $$1241$$ \, \cdot \, 65610751710320^{2} = 1$
$1243$ $171874$ $4875$ $171874^{2} \, - \, $$1243$$ \, \cdot \, 4875^{2} = 1$
$1245$ $7534241$ $213528$ $7534241^{2} \, - \, $$1245$$ \, \cdot \, 213528^{2} = 1$
$1246$ $443896693148735$ $12575431287288$ $443896693148735^{2} \, - \, $$1246$$ \, \cdot \, 12575431287288^{2} = 1$
$1247$ $929188$ $26313$ $929188^{2} \, - \, $$1247$$ \, \cdot \, 26313^{2} = 1$
$1249$ $170592135737332963602258146192126623188595201$ $4827005428364886233636226185917486870412640$ $170592135737332963602258146192126623188595201^{2} \, - \, $$1249$$ \, \cdot \, 4827005428364886233636226185917486870412640^{2} = 1$
$1253$ $2772351$ $78320$ $2772351^{2} \, - \, $$1253$$ \, \cdot \, 78320^{2} = 1$
$1254$ $362405$ $10234$ $362405^{2} \, - \, $$1254$$ \, \cdot \, 10234^{2} = 1$
$1255$ $31134002572889$ $878846634708$ $31134002572889^{2} \, - \, $$1255$$ \, \cdot \, 878846634708^{2} = 1$
$1257$ $101399$ $2860$ $101399^{2} \, - \, $$1257$$ \, \cdot \, 2860^{2} = 1$
$1258$ $26297959123$ $741449754$ $26297959123^{2} \, - \, $$1258$$ \, \cdot \, 741449754^{2} = 1$
$1259$ $111409143832810$ $3139843281069$ $111409143832810^{2} \, - \, $$1259$$ \, \cdot \, 3139843281069^{2} = 1$
$1261$ $121645306092343879707029626249$ $3425609167948170805090878900$ $121645306092343879707029626249^{2} \, - \, $$1261$$ \, \cdot \, 3425609167948170805090878900^{2} = 1$
$1262$ $61855669263$ $1741204708$ $61855669263^{2} \, - \, $$1262$$ \, \cdot \, 1741204708^{2} = 1$
$1263$ $142297$ $4004$ $142297^{2} \, - \, $$1263$$ \, \cdot \, 4004^{2} = 1$
$1265$ $206999$ $5820$ $206999^{2} \, - \, $$1265$$ \, \cdot \, 5820^{2} = 1$
$1266$ $533240465$ $14986708$ $533240465^{2} \, - \, $$1266$$ \, \cdot \, 14986708^{2} = 1$
$1267$ $625514462$ $17573127$ $625514462^{2} \, - \, $$1267$$ \, \cdot \, 17573127^{2} = 1$
$1270$ $581837113691$ $16326743118$ $581837113691^{2} \, - \, $$1270$$ \, \cdot \, 16326743118^{2} = 1$
$1271$ $32799$ $920$ $32799^{2} \, - \, $$1271$$ \, \cdot \, 920^{2} = 1$
$1273$ $183449440868134807$ $5141646215851476$ $183449440868134807^{2} \, - \, $$1273$$ \, \cdot \, 5141646215851476^{2} = 1$
$1277$ $41741976277195612208649$ $1168093368310765922740$ $41741976277195612208649^{2} \, - \, $$1277$$ \, \cdot \, 1168093368310765922740^{2} = 1$
$1279$ $2823156987094185989161256000$ $78940478828277833993575041$ $2823156987094185989161256000^{2} \, - \, $$1279$$ \, \cdot \, 78940478828277833993575041^{2} = 1$
$1281$ $790329175$ $22081748$ $790329175^{2} \, - \, $$1281$$ \, \cdot \, 22081748^{2} = 1$
$1282$ $3410326403$ $95247138$ $3410326403^{2} \, - \, $$1282$$ \, \cdot \, 95247138^{2} = 1$
$1283$ $1846514088226$ $51551261505$ $1846514088226^{2} \, - \, $$1283$$ \, \cdot \, 51551261505^{2} = 1$
$1285$ $154066218432467100261106249$ $4297895572464941510177100$ $154066218432467100261106249^{2} \, - \, $$1285$$ \, \cdot \, 4297895572464941510177100^{2} = 1$
$1286$ $25363110565$ $707264778$ $25363110565^{2} \, - \, $$1286$$ \, \cdot \, 707264778^{2} = 1$
$1289$ $180150127796503885363999220001$ $5017739558355166143865161400$ $180150127796503885363999220001^{2} \, - \, $$1289$$ \, \cdot \, 5017739558355166143865161400^{2} = 1$
$1290$ $431$ $12$ $431^{2} \, - \, $$1290$$ \, \cdot \, 12^{2} = 1$
$1291$ $709367533957910186877445608410$ $19742774580291798609489951267$ $709367533957910186877445608410^{2} \, - \, $$1291$$ \, \cdot \, 19742774580291798609489951267^{2} = 1$
$1293$ $863$ $24$ $863^{2} \, - \, $$1293$$ \, \cdot \, 24^{2} = 1$
$1294$ $1295$ $36$ $1295^{2} \, - \, $$1294$$ \, \cdot \, 36^{2} = 1$
$1295$ $36$ $1$ $36^{2} \, - \, $$1295$$ \, \cdot \, 1^{2} = 1$
$1297$ $2593$ $72$ $2593^{2} \, - \, $$1297$$ \, \cdot \, 72^{2} = 1$
$1298$ $1297$ $36$ $1297^{2} \, - \, $$1298$$ \, \cdot \, 36^{2} = 1$
$1299$ $865$ $24$ $865^{2} \, - \, $$1299$$ \, \cdot \, 24^{2} = 1$
$1301$ $94454226249$ $2618681900$ $94454226249^{2} \, - \, $$1301$$ \, \cdot \, 2618681900^{2} = 1$
$1302$ $433$ $12$ $433^{2} \, - \, $$1302$$ \, \cdot \, 12^{2} = 1$
$1303$ $36556474232606087113228808$ $1012726314518934688771461$ $36556474232606087113228808^{2} \, - \, $$1303$$ \, \cdot \, 1012726314518934688771461^{2} = 1$
$1306$ $194390104309027154137909530451$ $5379012634001634472555250670$ $194390104309027154137909530451^{2} \, - \, $$1306$$ \, \cdot \, 5379012634001634472555250670^{2} = 1$
$1307$ $195748082$ $5414517$ $195748082^{2} \, - \, $$1307$$ \, \cdot \, 5414517^{2} = 1$
$1309$ $803170174072265$ $22199221738044$ $803170174072265^{2} \, - \, $$1309$$ \, \cdot \, 22199221738044^{2} = 1$
$1310$ $125100021$ $3456382$ $125100021^{2} \, - \, $$1310$$ \, \cdot \, 3456382^{2} = 1$
$1311$ $193820$ $5353$ $193820^{2} \, - \, $$1311$$ \, \cdot \, 5353^{2} = 1$
$1313$ $758913$ $20944$ $758913^{2} \, - \, $$1313$$ \, \cdot \, 20944^{2} = 1$
$1315$ $887511646$ $24474351$ $887511646^{2} \, - \, $$1315$$ \, \cdot \, 24474351^{2} = 1$
$1317$ $37542877077093751$ $1034509930681500$ $37542877077093751^{2} \, - \, $$1317$$ \, \cdot \, 1034509930681500^{2} = 1$
$1318$ $11393611468262768176276517$ $313836679699540895794554$ $11393611468262768176276517^{2} \, - \, $$1318$$ \, \cdot \, 313836679699540895794554^{2} = 1$
$1319$ $1213059240$ $33401011$ $1213059240^{2} \, - \, $$1319$$ \, \cdot \, 33401011^{2} = 1$
$1321$ $5714003133469398668515586785344107222143861249$ $157213220905969449559233656682503745171415200$ $5714003133469398668515586785344107222143861249^{2} \, - \, $$1321$$ \, \cdot \, 157213220905969449559233656682503745171415200^{2} = 1$
$1322$ $1782164403$ $49015342$ $1782164403^{2} \, - \, $$1322$$ \, \cdot \, 49015342^{2} = 1$
$1326$ $2549$ $70$ $2549^{2} \, - \, $$1326$$ \, \cdot \, 70^{2} = 1$
$1327$ $65024$ $1785$ $65024^{2} \, - \, $$1327$$ \, \cdot \, 1785^{2} = 1$
$1329$ $704641456388201495$ $19328835950934116$ $704641456388201495^{2} \, - \, $$1329$$ \, \cdot \, 19328835950934116^{2} = 1$
$1330$ $1246589$ $34182$ $1246589^{2} \, - \, $$1330$$ \, \cdot \, 34182^{2} = 1$
$1333$ $330126493332151$ $9042016684140$ $330126493332151^{2} \, - \, $$1333$$ \, \cdot \, 9042016684140^{2} = 1$
$1334$ $3155972095$ $86408256$ $3155972095^{2} \, - \, $$1334$$ \, \cdot \, 86408256^{2} = 1$
$1335$ $45124$ $1235$ $45124^{2} \, - \, $$1335$$ \, \cdot \, 1235^{2} = 1$
$1337$ $1367431647$ $37397272$ $1367431647^{2} \, - \, $$1337$$ \, \cdot \, 37397272^{2} = 1$
$1338$ $17308813$ $473194$ $17308813^{2} \, - \, $$1338$$ \, \cdot \, 473194^{2} = 1$
$1339$ $150175$ $4104$ $150175^{2} \, - \, $$1339$$ \, \cdot \, 4104^{2} = 1$
$1342$ $1099$ $30$ $1099^{2} \, - \, $$1342$$ \, \cdot \, 30^{2} = 1$
$1343$ $388128$ $10591$ $388128^{2} \, - \, $$1343$$ \, \cdot \, 10591^{2} = 1$
$1345$ $4841$ $132$ $4841^{2} \, - \, $$1345$$ \, \cdot \, 132^{2} = 1$
$1346$ $340550115$ $9282362$ $340550115^{2} \, - \, $$1346$$ \, \cdot \, 9282362^{2} = 1$
$1347$ $6046682$ $164753$ $6046682^{2} \, - \, $$1347$$ \, \cdot \, 164753^{2} = 1$
$1349$ $2039180665951$ $55520034840$ $2039180665951^{2} \, - \, $$1349$$ \, \cdot \, 55520034840^{2} = 1$
$1351$ $6175$ $168$ $6175^{2} \, - \, $$1351$$ \, \cdot \, 168^{2} = 1$
$1353$ $42982433$ $1168536$ $42982433^{2} \, - \, $$1353$$ \, \cdot \, 1168536^{2} = 1$
$1354$ $346105897748788220212734451$ $9405885067178313198370290$ $346105897748788220212734451^{2} \, - \, $$1354$$ \, \cdot \, 9405885067178313198370290^{2} = 1$
$1355$ $1823289$ $49532$ $1823289^{2} \, - \, $$1355$$ \, \cdot \, 49532^{2} = 1$
$1357$ $355593479414372351$ $9653034643064640$ $355593479414372351^{2} \, - \, $$1357$$ \, \cdot \, 9653034643064640^{2} = 1$
$1358$ $2999823$ $81404$ $2999823^{2} \, - \, $$1358$$ \, \cdot \, 81404^{2} = 1$
$1361$ $351475875811710155440935201$ $9527225818589057344845080$ $351475875811710155440935201^{2} \, - \, $$1361$$ \, \cdot \, 9527225818589057344845080^{2} = 1$
$1362$ $1370184257$ $37127048$ $1370184257^{2} \, - \, $$1362$$ \, \cdot \, 37127048^{2} = 1$
$1363$ $3451726$ $93495$ $3451726^{2} \, - \, $$1363$$ \, \cdot \, 93495^{2} = 1$
$1365$ $25271$ $684$ $25271^{2} \, - \, $$1365$$ \, \cdot \, 684^{2} = 1$
$1366$ $2291037052846189335142389540899525$ $61987877112128467931286485364042$ $2291037052846189335142389540899525^{2} \, - \, $$1366$$ \, \cdot \, 61987877112128467931286485364042^{2} = 1$
$1367$ $1368$ $37$ $1368^{2} \, - \, $$1367$$ \, \cdot \, 37^{2} = 1$
$1370$ $2739$ $74$ $2739^{2} \, - \, $$1370$$ \, \cdot \, 74^{2} = 1$
$1371$ $1370$ $37$ $1370^{2} \, - \, $$1371$$ \, \cdot \, 37^{2} = 1$
$1373$ $1288491849$ $34773340$ $1288491849^{2} \, - \, $$1373$$ \, \cdot \, 34773340^{2} = 1$
$1374$ $153544325045$ $4142289074$ $153544325045^{2} \, - \, $$1374$$ \, \cdot \, 4142289074^{2} = 1$
$1378$ $3663851203$ $98699106$ $3663851203^{2} \, - \, $$1378$$ \, \cdot \, 98699106^{2} = 1$
$1379$ $2517968895$ $67806016$ $2517968895^{2} \, - \, $$1379$$ \, \cdot \, 67806016^{2} = 1$
$1381$ $91889645003972654622127399341267476203024769394634584316300287049$ $2472690352775053537868141555978544119564691977342423075952738420$ $91889645003972654622127399341267476203024769394634584316300287049^{2} \, - \, $$1381$$ \, \cdot \, 2472690352775053537868141555978544119564691977342423075952738420^{2} = 1$
$1382$ $13003237$ $349782$ $13003237^{2} \, - \, $$1382$$ \, \cdot \, 349782^{2} = 1$
$1383$ $1294948$ $34821$ $1294948^{2} \, - \, $$1383$$ \, \cdot \, 34821^{2} = 1$
$1385$ $21670288929$ $582290648$ $21670288929^{2} \, - \, $$1385$$ \, \cdot \, 582290648^{2} = 1$
$1387$ $1510442$ $40557$ $1510442^{2} \, - \, $$1387$$ \, \cdot \, 40557^{2} = 1$
$1389$ $625975$ $16796$ $625975^{2} \, - \, $$1389$$ \, \cdot \, 16796^{2} = 1$
$1390$ $2298622285432981$ $61653851607582$ $2298622285432981^{2} \, - \, $$1390$$ \, \cdot \, 61653851607582^{2} = 1$
$1391$ $9081305$ $243492$ $9081305^{2} \, - \, $$1391$$ \, \cdot \, 243492^{2} = 1$
$1393$ $3583$ $96$ $3583^{2} \, - \, $$1393$$ \, \cdot \, 96^{2} = 1$
$1394$ $12545$ $336$ $12545^{2} \, - \, $$1394$$ \, \cdot \, 336^{2} = 1$
$1397$ $16033248351$ $428966440$ $16033248351^{2} \, - \, $$1397$$ \, \cdot \, 428966440^{2} = 1$
$1398$ $4866437$ $130154$ $4866437^{2} \, - \, $$1398$$ \, \cdot \, 130154^{2} = 1$
$1399$ $72267866478994045309640$ $1932130144300442015349$ $72267866478994045309640^{2} \, - \, $$1399$$ \, \cdot \, 1932130144300442015349^{2} = 1$
$1401$ $1653779660151229685015$ $44183343633378497932$ $1653779660151229685015^{2} \, - \, $$1401$$ \, \cdot \, 44183343633378497932^{2} = 1$
$1402$ $1729858406386491965718163$ $46199422791797974269522$ $1729858406386491965718163^{2} \, - \, $$1402$$ \, \cdot \, 46199422791797974269522^{2} = 1$
$1403$ $74726$ $1995$ $74726^{2} \, - \, $$1403$$ \, \cdot \, 1995^{2} = 1$
$1405$ $2249$ $60$ $2249^{2} \, - \, $$1405$$ \, \cdot \, 60^{2} = 1$
$1406$ $75$ $2$ $75^{2} \, - \, $$1406$$ \, \cdot \, 2^{2} = 1$
$1407$ $3751$ $100$ $3751^{2} \, - \, $$1407$$ \, \cdot \, 100^{2} = 1$
$1409$ $2515181276570874689623012210848801$ $67006015714662899288959142526920$ $2515181276570874689623012210848801^{2} \, - \, $$1409$$ \, \cdot \, 67006015714662899288959142526920^{2} = 1$
$1410$ $751$ $20$ $751^{2} \, - \, $$1410$$ \, \cdot \, 20^{2} = 1$
$1411$ $444071330$ $11821953$ $444071330^{2} \, - \, $$1411$$ \, \cdot \, 11821953^{2} = 1$
$1414$ $182475063042299$ $4852648311810$ $182475063042299^{2} \, - \, $$1414$$ \, \cdot \, 4852648311810^{2} = 1$
$1415$ $22029004$ $585621$ $22029004^{2} \, - \, $$1415$$ \, \cdot \, 585621^{2} = 1$
$1417$ $5380608104297224993$ $142937583715450488$ $5380608104297224993^{2} \, - \, $$1417$$ \, \cdot \, 142937583715450488^{2} = 1$
$1418$ $3026264403$ $80365334$ $3026264403^{2} \, - \, $$1418$$ \, \cdot \, 80365334^{2} = 1$
$1419$ $12770$ $339$ $12770^{2} \, - \, $$1419$$ \, \cdot \, 339^{2} = 1$
$1423$ $480011423186147603704208$ $12724746017155626396759$ $480011423186147603704208^{2} \, - \, $$1423$$ \, \cdot \, 12724746017155626396759^{2} = 1$
$1426$ $9860975$ $261132$ $9860975^{2} \, - \, $$1426$$ \, \cdot \, 261132^{2} = 1$
$1427$ $9373918762$ $248147097$ $9373918762^{2} \, - \, $$1427$$ \, \cdot \, 248147097^{2} = 1$
$1429$ $22793644685449$ $602972713980$ $22793644685449^{2} \, - \, $$1429$$ \, \cdot \, 602972713980^{2} = 1$
$1430$ $13311$ $352$ $13311^{2} \, - \, $$1430$$ \, \cdot \, 352^{2} = 1$
$1433$ $66524184290667832353$ $1757342704595433176$ $66524184290667832353^{2} \, - \, $$1433$$ \, \cdot \, 1757342704595433176^{2} = 1$
$1434$ $176669098751$ $4665369200$ $176669098751^{2} \, - \, $$1434$$ \, \cdot \, 4665369200^{2} = 1$
$1435$ $999046$ $26373$ $999046^{2} \, - \, $$1435$$ \, \cdot \, 26373^{2} = 1$
$1437$ $97359338210399$ $2568320564040$ $97359338210399^{2} \, - \, $$1437$$ \, \cdot \, 2568320564040^{2} = 1$
$1438$ $15960728127743$ $420894506064$ $15960728127743^{2} \, - \, $$1438$$ \, \cdot \, 420894506064^{2} = 1$
$1439$ $12857985170030364960$ $338955373761021521$ $12857985170030364960^{2} \, - \, $$1439$$ \, \cdot \, 338955373761021521^{2} = 1$
$1441$ $841014472843068524054999$ $22154985959533110482700$ $841014472843068524054999^{2} \, - \, $$1441$$ \, \cdot \, 22154985959533110482700^{2} = 1$
$1442$ $1443$ $38$ $1443^{2} \, - \, $$1442$$ \, \cdot \, 38^{2} = 1$
$1443$ $38$ $1$ $38^{2} \, - \, $$1443$$ \, \cdot \, 1^{2} = 1$
$1446$ $1445$ $38$ $1445^{2} \, - \, $$1446$$ \, \cdot \, 38^{2} = 1$
$1447$ $130410331757421848$ $3428291438910093$ $130410331757421848^{2} \, - \, $$1447$$ \, \cdot \, 3428291438910093^{2} = 1$
$1451$ $32507827844328530$ $853403156620707$ $32507827844328530^{2} \, - \, $$1451$$ \, \cdot \, 853403156620707^{2} = 1$
$1453$ $410437909280225285392045277163541936816200282681664800649$ $10767494523648864494064975684283690243920830620634227020$ $410437909280225285392045277163541936816200282681664800649^{2} \, - \, $$1453$$ \, \cdot \, 10767494523648864494064975684283690243920830620634227020^{2} = 1$
$1454$ $366707758095$ $9616961884$ $366707758095^{2} \, - \, $$1454$$ \, \cdot \, 9616961884^{2} = 1$
$1455$ $23764$ $623$ $23764^{2} \, - \, $$1455$$ \, \cdot \, 623^{2} = 1$
$1457$ $7233162836703$ $189495310312$ $7233162836703^{2} \, - \, $$1457$$ \, \cdot \, 189495310312^{2} = 1$
$1459$ $98143956337994034503281010$ $2569424820981242287252281$ $98143956337994034503281010^{2} \, - \, $$1459$$ \, \cdot \, 2569424820981242287252281^{2} = 1$
$1461$ $416529161979728987575$ $10897335066584502228$ $416529161979728987575^{2} \, - \, $$1461$$ \, \cdot \, 10897335066584502228^{2} = 1$
$1462$ $2753$ $72$ $2753^{2} \, - \, $$1462$$ \, \cdot \, 72^{2} = 1$
$1463$ $153$ $4$ $153^{2} \, - \, $$1463$$ \, \cdot \, 4^{2} = 1$
$1465$ $1347185567591142710089249$ $35197239977950541355240$ $1347185567591142710089249^{2} \, - \, $$1465$$ \, \cdot \, 35197239977950541355240^{2} = 1$
$1466$ $47033698184547699$ $1228406604685910$ $47033698184547699^{2} \, - \, $$1466$$ \, \cdot \, 1228406604685910^{2} = 1$
$1469$ $760265$ $19836$ $760265^{2} \, - \, $$1469$$ \, \cdot \, 19836^{2} = 1$
$1471$ $39010573734728288548756018366160$ $1017128916397276238715671536737$ $39010573734728288548756018366160^{2} \, - \, $$1471$$ \, \cdot \, 1017128916397276238715671536737^{2} = 1$
$1473$ $2658699293399$ $69273614220$ $2658699293399^{2} \, - \, $$1473$$ \, \cdot \, 69273614220^{2} = 1$
$1474$ $54959576050729745$ $1431510810979476$ $54959576050729745^{2} \, - \, $$1474$$ \, \cdot \, 1431510810979476^{2} = 1$
$1477$ $10055043780174150436351$ $261633721214706222240$ $10055043780174150436351^{2} \, - \, $$1477$$ \, \cdot \, 261633721214706222240^{2} = 1$
$1478$ $119717$ $3114$ $119717^{2} \, - \, $$1478$$ \, \cdot \, 3114^{2} = 1$
$1479$ $4404376$ $114525$ $4404376^{2} \, - \, $$1479$$ \, \cdot \, 114525^{2} = 1$
$1481$ $3078401222921030518510235626262049$ $79992209653108287396849617045080$ $3078401222921030518510235626262049^{2} \, - \, $$1481$$ \, \cdot \, 79992209653108287396849617045080^{2} = 1$
$1482$ $77$ $2$ $77^{2} \, - \, $$1482$$ \, \cdot \, 2^{2} = 1$
$1483$ $158695889009423019181226$ $4120928705704463238045$ $158695889009423019181226^{2} \, - \, $$1483$$ \, \cdot \, 4120928705704463238045^{2} = 1$
$1486$ $18974735$ $492228$ $18974735^{2} \, - \, $$1486$$ \, \cdot \, 492228^{2} = 1$
$1487$ $7924224$ $205495$ $7924224^{2} \, - \, $$1487$$ \, \cdot \, 205495^{2} = 1$
$1489$ $19794264626972449$ $512970066248280$ $19794264626972449^{2} \, - \, $$1489$$ \, \cdot \, 512970066248280^{2} = 1$
$1490$ $74499$ $1930$ $74499^{2} \, - \, $$1490$$ \, \cdot \, 1930^{2} = 1$
$1491$ $68230$ $1767$ $68230^{2} \, - \, $$1491$$ \, \cdot \, 1767^{2} = 1$
$1493$ $85729041586288866249$ $2218697350071605900$ $85729041586288866249^{2} \, - \, $$1493$$ \, \cdot \, 2218697350071605900^{2} = 1$
$1495$ $116$ $3$ $116^{2} \, - \, $$1495$$ \, \cdot \, 3^{2} = 1$
$1497$ $22516718751127$ $581961430932$ $22516718751127^{2} \, - \, $$1497$$ \, \cdot \, 581961430932^{2} = 1$
$1498$ $321700659967$ $8311818384$ $321700659967^{2} \, - \, $$1498$$ \, \cdot \, 8311818384^{2} = 1$
$1499$ $3002576946562695360610$ $77552058394306780299$ $3002576946562695360610^{2} \, - \, $$1499$$ \, \cdot \, 77552058394306780299^{2} = 1$
$1501$ $13534735238019723614555987551$ $349348930906018990606250760$ $13534735238019723614555987551^{2} \, - \, $$1501$$ \, \cdot \, 349348930906018990606250760^{2} = 1$
$1502$ $5966017599$ $153939320$ $5966017599^{2} \, - \, $$1502$$ \, \cdot \, 153939320^{2} = 1$
$1505$ $11968361$ $308508$ $11968361^{2} \, - \, $$1505$$ \, \cdot \, 308508^{2} = 1$
$1506$ $31880816705$ $821517752$ $31880816705^{2} \, - \, $$1506$$ \, \cdot \, 821517752^{2} = 1$
$1507$ $4893778$ $126063$ $4893778^{2} \, - \, $$1507$$ \, \cdot \, 126063^{2} = 1$
$1509$ $64393055$ $1657656$ $64393055^{2} \, - \, $$1509$$ \, \cdot \, 1657656^{2} = 1$
$1510$ $84053391679$ $2163051048$ $84053391679^{2} \, - \, $$1510$$ \, \cdot \, 2163051048^{2} = 1$
$1511$ $38459732591163960$ $989404834498003$ $38459732591163960^{2} \, - \, $$1511$$ \, \cdot \, 989404834498003^{2} = 1$
$1513$ $22280499233$ $572803224$ $22280499233^{2} \, - \, $$1513$$ \, \cdot \, 572803224^{2} = 1$
$1514$ $5151268521999699$ $132388801787270$ $5151268521999699^{2} \, - \, $$1514$$ \, \cdot \, 132388801787270^{2} = 1$
$1515$ $506$ $13$ $506^{2} \, - \, $$1515$$ \, \cdot \, 13^{2} = 1$
$1517$ $29601$ $760$ $29601^{2} \, - \, $$1517$$ \, \cdot \, 760^{2} = 1$
$1518$ $1013$ $26$ $1013^{2} \, - \, $$1518$$ \, \cdot \, 26^{2} = 1$
$1522$ $3043$ $78$ $3043^{2} \, - \, $$1522$$ \, \cdot \, 78^{2} = 1$
$1523$ $1522$ $39$ $1522^{2} \, - \, $$1523$$ \, \cdot \, 39^{2} = 1$
$1526$ $102135615$ $2614568$ $102135615^{2} \, - \, $$1526$$ \, \cdot \, 2614568^{2} = 1$
$1527$ $508$ $13$ $508^{2} \, - \, $$1527$$ \, \cdot \, 13^{2} = 1$
$1529$ $72285400494999$ $1848616601300$ $72285400494999^{2} \, - \, $$1529$$ \, \cdot \, 1848616601300^{2} = 1$
$1531$ $1157070504812569705163513222450$ $29571423275371204812741659877$ $1157070504812569705163513222450^{2} \, - \, $$1531$$ \, \cdot \, 29571423275371204812741659877^{2} = 1$
$1533$ $65935351$ $1684020$ $65935351^{2} \, - \, $$1533$$ \, \cdot \, 1684020^{2} = 1$
$1534$ $235$ $6$ $235^{2} \, - \, $$1534$$ \, \cdot \, 6^{2} = 1$
$1535$ $1378124$ $35175$ $1378124^{2} \, - \, $$1535$$ \, \cdot \, 35175^{2} = 1$
$1537$ $75080329577$ $1915090212$ $75080329577^{2} \, - \, $$1537$$ \, \cdot \, 1915090212^{2} = 1$
$1538$ $813603$ $20746$ $813603^{2} \, - \, $$1538$$ \, \cdot \, 20746^{2} = 1$
$1541$ $832350906580405815$ $21203381993734892$ $832350906580405815^{2} \, - \, $$1541$$ \, \cdot \, 21203381993734892^{2} = 1$
$1542$ $2592101$ $66010$ $2592101^{2} \, - \, $$1542$$ \, \cdot \, 66010^{2} = 1$
$1543$ $6643215129085261568619128$ $169120149360850062054141$ $6643215129085261568619128^{2} \, - \, $$1543$$ \, \cdot \, 169120149360850062054141^{2} = 1$
$1545$ $123481961$ $3141516$ $123481961^{2} \, - \, $$1545$$ \, \cdot \, 3141516^{2} = 1$
$1546$ $3802792051$ $96715890$ $3802792051^{2} \, - \, $$1546$$ \, \cdot \, 96715890^{2} = 1$
$1547$ $118$ $3$ $118^{2} \, - \, $$1547$$ \, \cdot \, 3^{2} = 1$
$1549$ $48106848972197087743588687481413975084698632248110750633952591202305801$ $1222309542826747495934242683346380508818076263178681966098672827963220$ $48106848972197087743588687481413975084698632248110750633952591202305801^{2} \, - \, $$1549$$ \, \cdot \, 1222309542826747495934242683346380508818076263178681966098672827963220^{2} = 1$
$1551$ $1850201$ $46980$ $1850201^{2} \, - \, $$1551$$ \, \cdot \, 46980^{2} = 1$
$1553$ $16865536001301633$ $427971077468464$ $16865536001301633^{2} \, - \, $$1553$$ \, \cdot \, 427971077468464^{2} = 1$
$1554$ $160285$ $4066$ $160285^{2} \, - \, $$1554$$ \, \cdot \, 4066^{2} = 1$
$1555$ $5117847907209209$ $129784305853476$ $5117847907209209^{2} \, - \, $$1555$$ \, \cdot \, 129784305853476^{2} = 1$
$1558$ $17873016101$ $452808030$ $17873016101^{2} \, - \, $$1558$$ \, \cdot \, 452808030^{2} = 1$
$1559$ $2122635541940760$ $53759147640581$ $2122635541940760^{2} \, - \, $$1559$$ \, \cdot \, 53759147640581^{2} = 1$
$1561$ $171407516109350655091252735$ $4338388198177894781607072$ $171407516109350655091252735^{2} \, - \, $$1561$$ \, \cdot \, 4338388198177894781607072^{2} = 1$
$1562$ $1813197$ $45878$ $1813197^{2} \, - \, $$1562$$ \, \cdot \, 45878^{2} = 1$
$1563$ $24054459026$ $608437685$ $24054459026^{2} \, - \, $$1563$$ \, \cdot \, 608437685^{2} = 1$
$1565$ $467897169491706249$ $11827507906169900$ $467897169491706249^{2} \, - \, $$1565$$ \, \cdot \, 11827507906169900^{2} = 1$
$1567$ $2634128$ $66543$ $2634128^{2} \, - \, $$1567$$ \, \cdot \, 66543^{2} = 1$
$1569$ $3674077401859095458455$ $92754893170353950236$ $3674077401859095458455^{2} \, - \, $$1569$$ \, \cdot \, 92754893170353950236^{2} = 1$
$1570$ $287696384061859$ $7260801722778$ $287696384061859^{2} \, - \, $$1570$$ \, \cdot \, 7260801722778^{2} = 1$
$1571$ $1430064397610$ $36080080863$ $1430064397610^{2} \, - \, $$1571$$ \, \cdot \, 36080080863^{2} = 1$
$1574$ $3097184950960165$ $78066512141574$ $3097184950960165^{2} \, - \, $$1574$$ \, \cdot \, 78066512141574^{2} = 1$
$1577$ $112326799954263$ $2828573966428$ $112326799954263^{2} \, - \, $$1577$$ \, \cdot \, 2828573966428^{2} = 1$
$1578$ $442367$ $11136$ $442367^{2} \, - \, $$1578$$ \, \cdot \, 11136^{2} = 1$
$1579$ $852876982639022059460736831316490$ $21463242324201893177981952219891$ $852876982639022059460736831316490^{2} \, - \, $$1579$$ \, \cdot \, 21463242324201893177981952219891^{2} = 1$
$1581$ $291090185$ $7320852$ $291090185^{2} \, - \, $$1581$$ \, \cdot \, 7320852^{2} = 1$
$1582$ $8593649$ $216060$ $8593649^{2} \, - \, $$1582$$ \, \cdot \, 216060^{2} = 1$
$1583$ $94312707829728$ $2370444310151$ $94312707829728^{2} \, - \, $$1583$$ \, \cdot \, 2370444310151^{2} = 1$
$1585$ $318341744070762403104769$ $7996113646631818744896$ $318341744070762403104769^{2} \, - \, $$1585$$ \, \cdot \, 7996113646631818744896^{2} = 1$
$1586$ $335042499$ $8412950$ $335042499^{2} \, - \, $$1586$$ \, \cdot \, 8412950^{2} = 1$
$1589$ $126866457849998708855$ $3182620572954663804$ $126866457849998708855^{2} \, - \, $$1589$$ \, \cdot \, 3182620572954663804^{2} = 1$
$1590$ $319$ $8$ $319^{2} \, - \, $$1590$$ \, \cdot \, 8^{2} = 1$
$1591$ $11540919718817324$ $289337903407635$ $11540919718817324^{2} \, - \, $$1591$$ \, \cdot \, 289337903407635^{2} = 1$
$1594$ $1096489048689708486929226451$ $27463769151288592914799710$ $1096489048689708486929226451^{2} \, - \, $$1594$$ \, \cdot \, 27463769151288592914799710^{2} = 1$
$1595$ $639$ $16$ $639^{2} \, - \, $$1595$$ \, \cdot \, 16^{2} = 1$
$1597$ $519711527755463096224266385375638449943026746249$ $13004986088790772250309504643908671520836229100$ $519711527755463096224266385375638449943026746249^{2} \, - \, $$1597$$ \, \cdot \, 13004986088790772250309504643908671520836229100^{2} = 1$
$1598$ $1599$ $40$ $1599^{2} \, - \, $$1598$$ \, \cdot \, 40^{2} = 1$
$1599$ $40$ $1$ $40^{2} \, - \, $$1599$$ \, \cdot \, 1^{2} = 1$
$1601$ $3201$ $80$ $3201^{2} \, - \, $$1601$$ \, \cdot \, 80^{2} = 1$
$1603$ $72515603726$ $1811192895$ $72515603726^{2} \, - \, $$1603$$ \, \cdot \, 1811192895^{2} = 1$
$1605$ $641$ $16$ $641^{2} \, - \, $$1605$$ \, \cdot \, 16^{2} = 1$
$1606$ $24538370918885$ $612312261798$ $24538370918885^{2} \, - \, $$1606$$ \, \cdot \, 612312261798^{2} = 1$
$1607$ $137050219854024$ $3418785065885$ $137050219854024^{2} \, - \, $$1607$$ \, \cdot \, 3418785065885^{2} = 1$
$1609$ $106239618545424991765243316655636841919665809723452449$ $2648551857407766364935405630459204820419664252354920$ $106239618545424991765243316655636841919665809723452449^{2} \, - \, $$1609$$ \, \cdot \, 2648551857407766364935405630459204820419664252354920^{2} = 1$
$1610$ $321$ $8$ $321^{2} \, - \, $$1610$$ \, \cdot \, 8^{2} = 1$
$1613$ $4416393$ $109964$ $4416393^{2} \, - \, $$1613$$ \, \cdot \, 109964^{2} = 1$
$1614$ $291698879051$ $7260775270$ $291698879051^{2} \, - \, $$1614$$ \, \cdot \, 7260775270^{2} = 1$
$1615$ $3284569$ $81732$ $3284569^{2} \, - \, $$1615$$ \, \cdot \, 81732^{2} = 1$
$1618$ $2313310158883$ $57510164046$ $2313310158883^{2} \, - \, $$1618$$ \, \cdot \, 57510164046^{2} = 1$
$1619$ $78053433117061872410$ $1939851949127419161$ $78053433117061872410^{2} \, - \, $$1619$$ \, \cdot \, 1939851949127419161^{2} = 1$
$1621$ $6298101812493732343034974500091457815529942308667051412857352310169665125001$ $156429324369979112128445583345098338627552043874824108399177922442751050500$ $6298101812493732343034974500091457815529942308667051412857352310169665125001^{2} \, - \, $$1621$$ \, \cdot \, 156429324369979112128445583345098338627552043874824108399177922442751050500^{2} = 1$
$1622$ $2831176412101$ $70297763190$ $2831176412101^{2} \, - \, $$1622$$ \, \cdot \, 70297763190^{2} = 1$
$1623$ $53017$ $1316$ $53017^{2} \, - \, $$1623$$ \, \cdot \, 1316^{2} = 1$
$1626$ $266647183921549$ $6612668183130$ $266647183921549^{2} \, - \, $$1626$$ \, \cdot \, 6612668183130^{2} = 1$
$1627$ $14642$ $363$ $14642^{2} \, - \, $$1627$$ \, \cdot \, 363^{2} = 1$
$1630$ $15078465611$ $373476558$ $15078465611^{2} \, - \, $$1630$$ \, \cdot \, 373476558^{2} = 1$
$1631$ $39376$ $975$ $39376^{2} \, - \, $$1631$$ \, \cdot \, 975^{2} = 1$
$1633$ $329993200416163472690687$ $8166047445137789303136$ $329993200416163472690687^{2} \, - \, $$1633$$ \, \cdot \, 8166047445137789303136^{2} = 1$
$1634$ $24720785$ $611556$ $24720785^{2} \, - \, $$1634$$ \, \cdot \, 611556^{2} = 1$
$1635$ $115321$ $2852$ $115321^{2} \, - \, $$1635$$ \, \cdot \, 2852^{2} = 1$
$1637$ $14502382675358453346249$ $358438805194633965100$ $14502382675358453346249^{2} \, - \, $$1637$$ \, \cdot \, 358438805194633965100^{2} = 1$
$1639$ $1401940$ $34629$ $1401940^{2} \, - \, $$1639$$ \, \cdot \, 34629^{2} = 1$
$1641$ $4375$ $108$ $4375^{2} \, - \, $$1641$$ \, \cdot \, 108^{2} = 1$
$1642$ $2849294043676512198199390483$ $70315439208370501553286858$ $2849294043676512198199390483^{2} \, - \, $$1642$$ \, \cdot \, 70315439208370501553286858^{2} = 1$
$1643$ $8958$ $221$ $8958^{2} \, - \, $$1643$$ \, \cdot \, 221^{2} = 1$
$1645$ $9460519131041$ $233255566728$ $9460519131041^{2} \, - \, $$1645$$ \, \cdot \, 233255566728^{2} = 1$
$1646$ $80655$ $1988$ $80655^{2} \, - \, $$1646$$ \, \cdot \, 1988^{2} = 1$
$1649$ $23694502880412801$ $583495181032880$ $23694502880412801^{2} \, - \, $$1649$$ \, \cdot \, 583495181032880^{2} = 1$
$1651$ $56161343343007135$ $1382177919146568$ $56161343343007135^{2} \, - \, $$1651$$ \, \cdot \, 1382177919146568^{2} = 1$
$1653$ $1440734849$ $35436240$ $1440734849^{2} \, - \, $$1653$$ \, \cdot \, 35436240^{2} = 1$
$1654$ $14885$ $366$ $14885^{2} \, - \, $$1654$$ \, \cdot \, 366^{2} = 1$
$1655$ $320409$ $7876$ $320409^{2} \, - \, $$1655$$ \, \cdot \, 7876^{2} = 1$
$1657$ $230089311110767526480728245224891806849$ $5652429959428489976269630864789895280$ $230089311110767526480728245224891806849^{2} \, - \, $$1657$$ \, \cdot \, 5652429959428489976269630864789895280^{2} = 1$
$1658$ $3817806963$ $93760886$ $3817806963^{2} \, - \, $$1658$$ \, \cdot \, 93760886^{2} = 1$
$1659$ $747655$ $18356$ $747655^{2} \, - \, $$1659$$ \, \cdot \, 18356^{2} = 1$
$1661$ $12416252642220275199$ $304653186299769440$ $12416252642220275199^{2} \, - \, $$1661$$ \, \cdot \, 304653186299769440^{2} = 1$
$1662$ $64353749$ $1578550$ $64353749^{2} \, - \, $$1662$$ \, \cdot \, 1578550^{2} = 1$
$1663$ $172548834009765974150624$ $4231222898258884355775$ $172548834009765974150624^{2} \, - \, $$1663$$ \, \cdot \, 4231222898258884355775^{2} = 1$
$1667$ $272140632242$ $6665390367$ $272140632242^{2} \, - \, $$1667$$ \, \cdot \, 6665390367^{2} = 1$
$1669$ $2340275266476287900450581841147662370297772626212288201$ $57284717328038737412405689988022934138392598249664340$ $2340275266476287900450581841147662370297772626212288201^{2} \, - \, $$1669$$ \, \cdot \, 57284717328038737412405689988022934138392598249664340^{2} = 1$
$1670$ $100045691$ $2448162$ $100045691^{2} \, - \, $$1670$$ \, \cdot \, 2448162^{2} = 1$
$1671$ $9558676$ $233835$ $9558676^{2} \, - \, $$1671$$ \, \cdot \, 233835^{2} = 1$
$1673$ $3178424641407$ $77707680976$ $3178424641407^{2} \, - \, $$1673$$ \, \cdot \, 77707680976^{2} = 1$
$1677$ $34399$ $840$ $34399^{2} \, - \, $$1677$$ \, \cdot \, 840^{2} = 1$
$1678$ $9777409878270240143$ $238686492939208596$ $9777409878270240143^{2} \, - \, $$1678$$ \, \cdot \, 238686492939208596^{2} = 1$
$1679$ $1680$ $41$ $1680^{2} \, - \, $$1679$$ \, \cdot \, 41^{2} = 1$
$1685$ $2383536969$ $58066004$ $2383536969^{2} \, - \, $$1685$$ \, \cdot \, 58066004^{2} = 1$
$1686$ $35350768325$ $860934422$ $35350768325^{2} \, - \, $$1686$$ \, \cdot \, 860934422^{2} = 1$
$1687$ $34655415003224$ $843749566395$ $34655415003224^{2} \, - \, $$1687$$ \, \cdot \, 843749566395^{2} = 1$
$1689$ $32165559846732699944855$ $782665679312412462996$ $32165559846732699944855^{2} \, - \, $$1689$$ \, \cdot \, 782665679312412462996^{2} = 1$
$1691$ $33501079090$ $814679883$ $33501079090^{2} \, - \, $$1691$$ \, \cdot \, 814679883^{2} = 1$
$1693$ $3347246173698861715400298156892411849$ $81350302974597900525875082210468540$ $3347246173698861715400298156892411849^{2} \, - \, $$1693$$ \, \cdot \, 81350302974597900525875082210468540^{2} = 1$
$1695$ $249616$ $6063$ $249616^{2} \, - \, $$1695$$ \, \cdot \, 6063^{2} = 1$
$1697$ $276165737906448719649$ $6703920821893618840$ $276165737906448719649^{2} \, - \, $$1697$$ \, \cdot \, 6703920821893618840^{2} = 1$
$1698$ $4947715601$ $120070380$ $4947715601^{2} \, - \, $$1698$$ \, \cdot \, 120070380^{2} = 1$
$1699$ $2743345037851573163040031857578450$ $66555468361862588059573967039601$ $2743345037851573163040031857578450^{2} \, - \, $$1699$$ \, \cdot \, 66555468361862588059573967039601^{2} = 1$
$1702$ $231069000116251$ $5600952727350$ $231069000116251^{2} \, - \, $$1702$$ \, \cdot \, 5600952727350^{2} = 1$
$1703$ $1937753$ $46956$ $1937753^{2} \, - \, $$1703$$ \, \cdot \, 46956^{2} = 1$
$1705$ $991$ $24$ $991^{2} \, - \, $$1705$$ \, \cdot \, 24^{2} = 1$
$1706$ $464962384640822451$ $11257146203165230$ $464962384640822451^{2} \, - \, $$1706$$ \, \cdot \, 11257146203165230^{2} = 1$
$1707$ $616226$ $14915$ $616226^{2} \, - \, $$1707$$ \, \cdot \, 14915^{2} = 1$
$1709$ $12275567551745514715418401801688716704201$ $296941261474754418895689188431662360740$ $12275567551745514715418401801688716704201^{2} \, - \, $$1709$$ \, \cdot \, 296941261474754418895689188431662360740^{2} = 1$
$1711$ $12257063847449$ $296320326540$ $12257063847449^{2} \, - \, $$1711$$ \, \cdot \, 296320326540^{2} = 1$
$1713$ $38597180060887$ $932560238356$ $38597180060887^{2} \, - \, $$1713$$ \, \cdot \, 932560238356^{2} = 1$
$1714$ $85699$ $2070$ $85699^{2} \, - \, $$1714$$ \, \cdot \, 2070^{2} = 1$
$1717$ $51713$ $1248$ $51713^{2} \, - \, $$1717$$ \, \cdot \, 1248^{2} = 1$
$1718$ $137592901$ $3319590$ $137592901^{2} \, - \, $$1718$$ \, \cdot \, 3319590^{2} = 1$
$1721$ $20146877307386204293940577255201$ $485643193698452138520439803320$ $20146877307386204293940577255201^{2} \, - \, $$1721$$ \, \cdot \, 485643193698452138520439803320^{2} = 1$
$1722$ $83$ $2$ $83^{2} \, - \, $$1722$$ \, \cdot \, 2^{2} = 1$
$1723$ $527541088010971890626$ $12709066495146742875$ $527541088010971890626^{2} \, - \, $$1723$$ \, \cdot \, 12709066495146742875^{2} = 1$
$1726$ $2689844967637183200753607543760431273535$ $64745092245111302274843632152698614232$ $2689844967637183200753607543760431273535^{2} \, - \, $$1726$$ \, \cdot \, 64745092245111302274843632152698614232^{2} = 1$
$1727$ $25433$ $612$ $25433^{2} \, - \, $$1727$$ \, \cdot \, 612^{2} = 1$
$1729$ $44611924489705$ $1072885712316$ $44611924489705^{2} \, - \, $$1729$$ \, \cdot \, 1072885712316^{2} = 1$
$1730$ $10632611139$ $255632978$ $10632611139^{2} \, - \, $$1730$$ \, \cdot \, 255632978^{2} = 1$
$1731$ $1666375$ $40052$ $1666375^{2} \, - \, $$1731$$ \, \cdot \, 40052^{2} = 1$
$1733$ $13121910625238042893028027475849$ $315208408380294046461405392740$ $13121910625238042893028027475849^{2} \, - \, $$1733$$ \, \cdot \, 315208408380294046461405392740^{2} = 1$
$1735$ $3124$ $75$ $3124^{2} \, - \, $$1735$$ \, \cdot \, 75^{2} = 1$
$1738$ $2801715696553663$ $67204627338744$ $2801715696553663^{2} \, - \, $$1738$$ \, \cdot \, 67204627338744^{2} = 1$
$1739$ $34520185$ $827796$ $34520185^{2} \, - \, $$1739$$ \, \cdot \, 827796^{2} = 1$
$1741$ $200732766003831003193006297682960023218244607119128428033893005001$ $4810817514964694733460371899299888507813254563349737403155528100$ $200732766003831003193006297682960023218244607119128428033893005001^{2} \, - \, $$1741$$ \, \cdot \, 4810817514964694733460371899299888507813254563349737403155528100^{2} = 1$
$1742$ $96747$ $2318$ $96747^{2} \, - \, $$1742$$ \, \cdot \, 2318^{2} = 1$
$1743$ $167$ $4$ $167^{2} \, - \, $$1743$$ \, \cdot \, 4^{2} = 1$
$1745$ $32837409$ $786088$ $32837409^{2} \, - \, $$1745$$ \, \cdot \, 786088^{2} = 1$
$1747$ $722692635222980474388116882$ $17290485040281059863874103$ $722692635222980474388116882^{2} \, - \, $$1747$$ \, \cdot \, 17290485040281059863874103^{2} = 1$
$1749$ $31356358199$ $749774580$ $31356358199^{2} \, - \, $$1749$$ \, \cdot \, 749774580^{2} = 1$
$1751$ $34815$ $832$ $34815^{2} \, - \, $$1751$$ \, \cdot \, 832^{2} = 1$
$1753$ $1619748562245139313693000103452757473032993$ $38686250985878460680927299688094405197496$ $1619748562245139313693000103452757473032993^{2} \, - \, $$1753$$ \, \cdot \, 38686250985878460680927299688094405197496^{2} = 1$
$1754$ $85240173975114903632499$ $2035305156619813089050$ $85240173975114903632499^{2} \, - \, $$1754$$ \, \cdot \, 2035305156619813089050^{2} = 1$
$1757$ $503$ $12$ $503^{2} \, - \, $$1757$$ \, \cdot \, 12^{2} = 1$
$1758$ $587$ $14$ $587^{2} \, - \, $$1758$$ \, \cdot \, 14^{2} = 1$
$1759$ $171219104308739629828563069290064892640$ $4082435210582013346732801540734333681$ $171219104308739629828563069290064892640^{2} \, - \, $$1759$$ \, \cdot \, 4082435210582013346732801540734333681^{2} = 1$
$1761$ $1175$ $28$ $1175^{2} \, - \, $$1761$$ \, \cdot \, 28^{2} = 1$
$1762$ $1763$ $42$ $1763^{2} \, - \, $$1762$$ \, \cdot \, 42^{2} = 1$
$1763$ $42$ $1$ $42^{2} \, - \, $$1763$$ \, \cdot \, 1^{2} = 1$
$1765$ $3529$ $84$ $3529^{2} \, - \, $$1765$$ \, \cdot \, 84^{2} = 1$
$1766$ $1765$ $42$ $1765^{2} \, - \, $$1766$$ \, \cdot \, 42^{2} = 1$
$1767$ $1177$ $28$ $1177^{2} \, - \, $$1767$$ \, \cdot \, 28^{2} = 1$
$1769$ $30905719492118049$ $734809803891160$ $30905719492118049^{2} \, - \, $$1769$$ \, \cdot \, 734809803891160^{2} = 1$
$1770$ $589$ $14$ $589^{2} \, - \, $$1770$$ \, \cdot \, 14^{2} = 1$
$1771$ $505$ $12$ $505^{2} \, - \, $$1771$$ \, \cdot \, 12^{2} = 1$
$1774$ $125288009537733004908595972131215$ $2974628275728557930834554244724$ $125288009537733004908595972131215^{2} \, - \, $$1774$$ \, \cdot \, 2974628275728557930834554244724^{2} = 1$
$1777$ $114654350050825314539681710339770969616513$ $2719861708389141746619218981337647759472$ $114654350050825314539681710339770969616513^{2} \, - \, $$1777$$ \, \cdot \, 2719861708389141746619218981337647759472^{2} = 1$
$1778$ $253$ $6$ $253^{2} \, - \, $$1778$$ \, \cdot \, 6^{2} = 1$
$1779$ $84624555410$ $2006357991$ $84624555410^{2} \, - \, $$1779$$ \, \cdot \, 2006357991^{2} = 1$
$1781$ $44128916375049$ $1045661946020$ $44128916375049^{2} \, - \, $$1781$$ \, \cdot \, 1045661946020^{2} = 1$
$1783$ $300574618222444417557224$ $7118305658345640812235$ $300574618222444417557224^{2} \, - \, $$1783$$ \, \cdot \, 7118305658345640812235^{2} = 1$
$1785$ $169$ $4$ $169^{2} \, - \, $$1785$$ \, \cdot \, 4^{2} = 1$
$1786$ $78064935471648262925$ $1847205775499723178$ $78064935471648262925^{2} \, - \, $$1786$$ \, \cdot \, 1847205775499723178^{2} = 1$
$1787$ $216226$ $5115$ $216226^{2} \, - \, $$1787$$ \, \cdot \, 5115^{2} = 1$
$1789$ $13673687937600285436522338047798889300505982960692087644059539022368201$ $323281233024712565221770716009156212819348235266978239649677477568260$ $13673687937600285436522338047798889300505982960692087644059539022368201^{2} \, - \, $$1789$$ \, \cdot \, 323281233024712565221770716009156212819348235266978239649677477568260^{2} = 1$
$1790$ $60501$ $1430$ $60501^{2} \, - \, $$1790$$ \, \cdot \, 1430^{2} = 1$
$1793$ $262535353551703$ $6200085091284$ $262535353551703^{2} \, - \, $$1793$$ \, \cdot \, 6200085091284^{2} = 1$
$1794$ $12582335$ $297064$ $12582335^{2} \, - \, $$1794$$ \, \cdot \, 297064^{2} = 1$
$1795$ $2389684563359$ $56403798408$ $2389684563359^{2} \, - \, $$1795$$ \, \cdot \, 56403798408^{2} = 1$
$1797$ $15908371013339999$ $375276761753400$ $15908371013339999^{2} \, - \, $$1797$$ \, \cdot \, 375276761753400^{2} = 1$
$1798$ $2089768622363$ $49283706246$ $2089768622363^{2} \, - \, $$1798$$ \, \cdot \, 49283706246^{2} = 1$
$1799$ $3024120$ $71299$ $3024120^{2} \, - \, $$1799$$ \, \cdot \, 71299^{2} = 1$
$1801$ $806667238174283887339603999510156079461856181188670036342049$ $19008049861749803182382268306718420151334269606450750222280$ $806667238174283887339603999510156079461856181188670036342049^{2} \, - \, $$1801$$ \, \cdot \, 19008049861749803182382268306718420151334269606450750222280^{2} = 1$
$1802$ $849$ $20$ $849^{2} \, - \, $$1802$$ \, \cdot \, 20^{2} = 1$
$1803$ $203137$ $4784$ $203137^{2} \, - \, $$1803$$ \, \cdot \, 4784^{2} = 1$
$1806$ $85$ $2$ $85^{2} \, - \, $$1806$$ \, \cdot \, 2^{2} = 1$
$1807$ $146471428766233$ $3445671269172$ $146471428766233^{2} \, - \, $$1807$$ \, \cdot \, 3445671269172^{2} = 1$
$1810$ $104491504202900419$ $2456075391002874$ $104491504202900419^{2} \, - \, $$1810$$ \, \cdot \, 2456075391002874^{2} = 1$
$1811$ $146690$ $3447$ $146690^{2} \, - \, $$1811$$ \, \cdot \, 3447^{2} = 1$
$1814$ $789064983271716805$ $18526531941823254$ $789064983271716805^{2} \, - \, $$1814$$ \, \cdot \, 18526531941823254^{2} = 1$
$1817$ $23937367869663$ $561563575352$ $23937367869663^{2} \, - \, $$1817$$ \, \cdot \, 561563575352^{2} = 1$
$1819$ $44077149500774570$ $1033468279123611$ $44077149500774570^{2} \, - \, $$1819$$ \, \cdot \, 1033468279123611^{2} = 1$
$1821$ $27895878625724240557523549815$ $653709914682473849947668012$ $27895878625724240557523549815^{2} \, - \, $$1821$$ \, \cdot \, 653709914682473849947668012^{2} = 1$
$1822$ $371368817235398339023103$ $8700240303998557258992$ $371368817235398339023103^{2} \, - \, $$1822$$ \, \cdot \, 8700240303998557258992^{2} = 1$
$1823$ $396777789408$ $9292958959$ $396777789408^{2} \, - \, $$1823$$ \, \cdot \, 9292958959^{2} = 1$
$1826$ $3069505$ $71832$ $3069505^{2} \, - \, $$1826$$ \, \cdot \, 71832^{2} = 1$
$1829$ $270242224363704372219999$ $6318970882787739474200$ $270242224363704372219999^{2} \, - \, $$1829$$ \, \cdot \, 6318970882787739474200^{2} = 1$
$1830$ $59291$ $1386$ $59291^{2} \, - \, $$1830$$ \, \cdot \, 1386^{2} = 1$
$1831$ $1918032733134113893633567757731959058040$ $44824127254720935022058326058303814477$ $1918032733134113893633567757731959058040^{2} \, - \, $$1831$$ \, \cdot \, 44824127254720935022058326058303814477^{2} = 1$
$1833$ $4253783$ $99356$ $4253783^{2} \, - \, $$1833$$ \, \cdot \, 99356^{2} = 1$
$1834$ $218268829391589325$ $5096735001878706$ $218268829391589325^{2} \, - \, $$1834$$ \, \cdot \, 5096735001878706^{2} = 1$
$1835$ $1097124846$ $25611677$ $1097124846^{2} \, - \, $$1835$$ \, \cdot \, 25611677^{2} = 1$
$1837$ $11896195389280834861151$ $277557847295851334520$ $11896195389280834861151^{2} \, - \, $$1837$$ \, \cdot \, 277557847295851334520^{2} = 1$
$1838$ $24564830389263$ $572982049244$ $24564830389263^{2} \, - \, $$1838$$ \, \cdot \, 572982049244^{2} = 1$
$1839$ $26133415$ $609404$ $26133415^{2} \, - \, $$1839$$ \, \cdot \, 609404^{2} = 1$
$1841$ $221708542820333535$ $5167203114643592$ $221708542820333535^{2} \, - \, $$1841$$ \, \cdot \, 5167203114643592^{2} = 1$
$1842$ $5057485457$ $117839212$ $5057485457^{2} \, - \, $$1842$$ \, \cdot \, 117839212^{2} = 1$
$1843$ $49871434404842$ $1161687167529$ $49871434404842^{2} \, - \, $$1843$$ \, \cdot \, 1161687167529^{2} = 1$
$1846$ $6289018486180795$ $146375038721562$ $6289018486180795^{2} \, - \, $$1846$$ \, \cdot \, 146375038721562^{2} = 1$
$1847$ $1848$ $43$ $1848^{2} \, - \, $$1847$$ \, \cdot \, 43^{2} = 1$
$1851$ $1850$ $43$ $1850^{2} \, - \, $$1851$$ \, \cdot \, 43^{2} = 1$
$1853$ $3170946249$ $73663300$ $3170946249^{2} \, - \, $$1853$$ \, \cdot \, 73663300^{2} = 1$
$1855$ $7373836$ $171207$ $7373836^{2} \, - \, $$1855$$ \, \cdot \, 171207^{2} = 1$
$1857$ $2384332526604623767$ $55330025645916772$ $2384332526604623767^{2} \, - \, $$1857$$ \, \cdot \, 55330025645916772^{2} = 1$
$1858$ $763416899$ $17710830$ $763416899^{2} \, - \, $$1858$$ \, \cdot \, 17710830^{2} = 1$
$1861$ $7077752008438005001$ $164067346843752900$ $7077752008438005001^{2} \, - \, $$1861$$ \, \cdot \, 164067346843752900^{2} = 1$
$1865$ $118187440929$ $2736729736$ $118187440929^{2} \, - \, $$1865$$ \, \cdot \, 2736729736^{2} = 1$
$1866$ $15551$ $360$ $15551^{2} \, - \, $$1866$$ \, \cdot \, 360^{2} = 1$
$1867$ $87726791690293922$ $2030299407245043$ $87726791690293922^{2} \, - \, $$1867$$ \, \cdot \, 2030299407245043^{2} = 1$
$1869$ $8510103765449$ $196847636580$ $8510103765449^{2} \, - \, $$1869$$ \, \cdot \, 196847636580^{2} = 1$
$1870$ $19682191$ $455148$ $19682191^{2} \, - \, $$1870$$ \, \cdot \, 455148^{2} = 1$
$1871$ $14960670347259644125807440$ $345871008137584484948087$ $14960670347259644125807440^{2} \, - \, $$1871$$ \, \cdot \, 345871008137584484948087^{2} = 1$
$1873$ $66646007780116951182547242065928991437872293825926433$ $1539945144498948869710411296974494665952998698040984$ $66646007780116951182547242065928991437872293825926433^{2} \, - \, $$1873$$ \, \cdot \, 1539945144498948869710411296974494665952998698040984^{2} = 1$
$1874$ $21455425$ $495624$ $21455425^{2} \, - \, $$1874$$ \, \cdot \, 495624^{2} = 1$
$1877$ $8483443124159168649$ $195812321451440260$ $8483443124159168649^{2} \, - \, $$1877$$ \, \cdot \, 195812321451440260^{2} = 1$
$1878$ $16901$ $390$ $16901^{2} \, - \, $$1878$$ \, \cdot \, 390^{2} = 1$
$1879$ $94345422639044420558808634792532120$ $2176493849722945361406489700835109$ $94345422639044420558808634792532120^{2} \, - \, $$1879$$ \, \cdot \, 2176493849722945361406489700835109^{2} = 1$
$1882$ $29814643$ $687258$ $29814643^{2} \, - \, $$1882$$ \, \cdot \, 687258^{2} = 1$
$1883$ $6726$ $155$ $6726^{2} \, - \, $$1883$$ \, \cdot \, 155^{2} = 1$
$1885$ $521$ $12$ $521^{2} \, - \, $$1885$$ \, \cdot \, 12^{2} = 1$
$1886$ $92415$ $2128$ $92415^{2} \, - \, $$1886$$ \, \cdot \, 2128^{2} = 1$
$1887$ $8992$ $207$ $8992^{2} \, - \, $$1887$$ \, \cdot \, 207^{2} = 1$
$1889$ $36981073720080844052144960978049$ $850870638559564006506264967760$ $36981073720080844052144960978049^{2} \, - \, $$1889$$ \, \cdot \, 850870638559564006506264967760^{2} = 1$
$1891$ $819136267782775550$ $18836941567957233$ $819136267782775550^{2} \, - \, $$1891$$ \, \cdot \, 18836941567957233^{2} = 1$
$1893$ $5047$ $116$ $5047^{2} \, - \, $$1893$$ \, \cdot \, 116^{2} = 1$
$1894$ $226309103832669021290704832069984034245$ $5200104096794640672678934313809609086$ $226309103832669021290704832069984034245^{2} \, - \, $$1894$$ \, \cdot \, 5200104096794640672678934313809609086^{2} = 1$
$1895$ $54849639$ $1259996$ $54849639^{2} \, - \, $$1895$$ \, \cdot \, 1259996^{2} = 1$
$1897$ $43903$ $1008$ $43903^{2} \, - \, $$1897$$ \, \cdot \, 1008^{2} = 1$
$1898$ $10662963$ $244754$ $10662963^{2} \, - \, $$1898$$ \, \cdot \, 244754^{2} = 1$
$1901$ $95049$ $2180$ $95049^{2} \, - \, $$1901$$ \, \cdot \, 2180^{2} = 1$
$1902$ $2846027$ $65258$ $2846027^{2} \, - \, $$1902$$ \, \cdot \, 65258^{2} = 1$
$1903$ $875034172$ $20058831$ $875034172^{2} \, - \, $$1903$$ \, \cdot \, 20058831^{2} = 1$
$1905$ $10709910761$ $245379548$ $10709910761^{2} \, - \, $$1905$$ \, \cdot \, 245379548^{2} = 1$
$1906$ $229206573179802193699$ $5250076359252217890$ $229206573179802193699^{2} \, - \, $$1906$$ \, \cdot \, 5250076359252217890^{2} = 1$
$1907$ $17162$ $393$ $17162^{2} \, - \, $$1907$$ \, \cdot \, 393^{2} = 1$
$1909$ $2380667255$ $54487356$ $2380667255^{2} \, - \, $$1909$$ \, \cdot \, 54487356^{2} = 1$
$1910$ $278479$ $6372$ $278479^{2} \, - \, $$1910$$ \, \cdot \, 6372^{2} = 1$
$1913$ $45099388699237198022388513$ $1031129401013034423392056$ $45099388699237198022388513^{2} \, - \, $$1913$$ \, \cdot \, 1031129401013034423392056^{2} = 1$
$1914$ $175$ $4$ $175^{2} \, - \, $$1914$$ \, \cdot \, 4^{2} = 1$
$1915$ $1027150205228001406$ $23471971442429307$ $1027150205228001406^{2} \, - \, $$1915$$ \, \cdot \, 23471971442429307^{2} = 1$
$1918$ $416753$ $9516$ $416753^{2} \, - \, $$1918$$ \, \cdot \, 9516^{2} = 1$
$1919$ $77244401049$ $1763313460$ $77244401049^{2} \, - \, $$1919$$ \, \cdot \, 1763313460^{2} = 1$
$1921$ $10192726099458738978050281249$ $232555530178603601325441000$ $10192726099458738978050281249^{2} \, - \, $$1921$$ \, \cdot \, 232555530178603601325441000^{2} = 1$
$1923$ $4367227226$ $99590095$ $4367227226^{2} \, - \, $$1923$$ \, \cdot \, 99590095^{2} = 1$
$1927$ $46636702417448$ $1062397346883$ $46636702417448^{2} \, - \, $$1927$$ \, \cdot \, 1062397346883^{2} = 1$
$1929$ $126794455$ $2886916$ $126794455^{2} \, - \, $$1929$$ \, \cdot \, 2886916^{2} = 1$
$1930$ $128648082263059$ $2928361322694$ $128648082263059^{2} \, - \, $$1930$$ \, \cdot \, 2928361322694^{2} = 1$
$1931$ $53405823410$ $1215339123$ $53405823410^{2} \, - \, $$1931$$ \, \cdot \, 1215339123^{2} = 1$
$1933$ $143801925919973973006746044614830462252244345987283849$ $3270760735371267636227864743687616171541802967004660$ $143801925919973973006746044614830462252244345987283849^{2} \, - \, $$1933$$ \, \cdot \, 3270760735371267636227864743687616171541802967004660^{2} = 1$
$1934$ $1935$ $44$ $1935^{2} \, - \, $$1934$$ \, \cdot \, 44^{2} = 1$
$1937$ $3873$ $88$ $3873^{2} \, - \, $$1937$$ \, \cdot \, 88^{2} = 1$
$1938$ $1937$ $44$ $1937^{2} \, - \, $$1938$$ \, \cdot \, 44^{2} = 1$
$1939$ $6672165474011915935$ $151522771012903896$ $6672165474011915935^{2} \, - \, $$1939$$ \, \cdot \, 151522771012903896^{2} = 1$
$1941$ $582709607499783953373016131935$ $13226331726483194685799879992$ $582709607499783953373016131935^{2} \, - \, $$1941$$ \, \cdot \, 13226331726483194685799879992^{2} = 1$
$1942$ $6984160935186866597$ $158485533243485118$ $6984160935186866597^{2} \, - \, $$1942$$ \, \cdot \, 158485533243485118^{2} = 1$
$1943$ $83751$ $1900$ $83751^{2} \, - \, $$1943$$ \, \cdot \, 1900^{2} = 1$
$1945$ $2632285113641$ $59686089372$ $2632285113641^{2} \, - \, $$1945$$ \, \cdot \, 59686089372^{2} = 1$
$1946$ $121257485$ $2748762$ $121257485^{2} \, - \, $$1946$$ \, \cdot \, 2748762^{2} = 1$
$1947$ $353$ $8$ $353^{2} \, - \, $$1947$$ \, \cdot \, 8^{2} = 1$
$1949$ $13850471049$ $313731860$ $13850471049^{2} \, - \, $$1949$$ \, \cdot \, 313731860^{2} = 1$
$1951$ $226742438218831488120936558859828640$ $5133389024333877559662473405561007$ $226742438218831488120936558859828640^{2} \, - \, $$1951$$ \, \cdot \, 5133389024333877559662473405561007^{2} = 1$
$1954$ $4691555$ $106134$ $4691555^{2} \, - \, $$1954$$ \, \cdot \, 106134^{2} = 1$
$1955$ $2874$ $65$ $2874^{2} \, - \, $$1955$$ \, \cdot \, 65^{2} = 1$
$1957$ $400881151$ $9061920$ $400881151^{2} \, - \, $$1957$$ \, \cdot \, 9061920^{2} = 1$
$1958$ $177$ $4$ $177^{2} \, - \, $$1958$$ \, \cdot \, 4^{2} = 1$
$1959$ $9719730001876$ $219602349925$ $9719730001876^{2} \, - \, $$1959$$ \, \cdot \, 219602349925^{2} = 1$
$1961$ $5431118185$ $122645172$ $5431118185^{2} \, - \, $$1961$$ \, \cdot \, 122645172^{2} = 1$
$1963$ $24445564472798$ $551746923459$ $24445564472798^{2} \, - \, $$1963$$ \, \cdot \, 551746923459^{2} = 1$
$1965$ $1176119$ $26532$ $1176119^{2} \, - \, $$1965$$ \, \cdot \, 26532^{2} = 1$
$1966$ $9850975268107008669640939861775$ $222171052269092942126897458308$ $9850975268107008669640939861775^{2} \, - \, $$1966$$ \, \cdot \, 222171052269092942126897458308^{2} = 1$
$1967$ $2528$ $57$ $2528^{2} \, - \, $$1967$$ \, \cdot \, 57^{2} = 1$
$1969$ $46885009158085926066844328473751$ $1056601315610203746069441327300$ $46885009158085926066844328473751^{2} \, - \, $$1969$$ \, \cdot \, 1056601315610203746069441327300^{2} = 1$
$1970$ $665859$ $15002$ $665859^{2} \, - \, $$1970$$ \, \cdot \, 15002^{2} = 1$
$1973$ $15673705353$ $352864636$ $15673705353^{2} \, - \, $$1973$$ \, \cdot \, 352864636^{2} = 1$
$1974$ $1376255$ $30976$ $1376255^{2} \, - \, $$1974$$ \, \cdot \, 30976^{2} = 1$
$1977$ $230201397518423$ $5177315380292$ $230201397518423^{2} \, - \, $$1977$$ \, \cdot \, 5177315380292^{2} = 1$
$1978$ $60973994702573$ $1370981217774$ $60973994702573^{2} \, - \, $$1978$$ \, \cdot \, 1370981217774^{2} = 1$
$1979$ $196956439969690$ $4427384992341$ $196956439969690^{2} \, - \, $$1979$$ \, \cdot \, 4427384992341^{2} = 1$
$1981$ $478731918732725530377313576551512366455$ $10755983977504786513343290157817764652$ $478731918732725530377313576551512366455^{2} \, - \, $$1981$$ \, \cdot \, 10755983977504786513343290157817764652^{2} = 1$
$1982$ $438784358463$ $9855968632$ $438784358463^{2} \, - \, $$1982$$ \, \cdot \, 9855968632^{2} = 1$
$1983$ $354724327$ $7965804$ $354724327^{2} \, - \, $$1983$$ \, \cdot \, 7965804^{2} = 1$
$1985$ $7277897861828346369$ $163352468178638816$ $7277897861828346369^{2} \, - \, $$1985$$ \, \cdot \, 163352468178638816^{2} = 1$
$1986$ $13209364625$ $296409628$ $13209364625^{2} \, - \, $$1986$$ \, \cdot \, 296409628^{2} = 1$
$1987$ $2163842$ $48543$ $2163842^{2} \, - \, $$1987$$ \, \cdot \, 48543^{2} = 1$
$1990$ $35314095433681999$ $791628731408580$ $35314095433681999^{2} \, - \, $$1990$$ \, \cdot \, 791628731408580^{2} = 1$
$1991$ $95638951$ $2143380$ $95638951^{2} \, - \, $$1991$$ \, \cdot \, 2143380^{2} = 1$
$1993$ $95533468778868471170054252659885376539035649$ $2139941483287135231593131558297490898854720$ $95533468778868471170054252659885376539035649^{2} \, - \, $$1993$$ \, \cdot \, 2139941483287135231593131558297490898854720^{2} = 1$
$1994$ $14178877526856051$ $317525986680530$ $14178877526856051^{2} \, - \, $$1994$$ \, \cdot \, 317525986680530^{2} = 1$
$1995$ $134$ $3$ $134^{2} \, - \, $$1995$$ \, \cdot \, 3^{2} = 1$
$1997$ $295547530063295123979849$ $6613605743817751666820$ $295547530063295123979849^{2} \, - \, $$1997$$ \, \cdot \, 6613605743817751666820^{2} = 1$
$1999$ $4027701399389138208695911951306886478800$ $90084665203202024260494303744425250249$ $4027701399389138208695911951306886478800^{2} \, - \, $$1999$$ \, \cdot \, 90084665203202024260494303744425250249^{2} = 1$