]> Fundamental Solutions to Pell's Equation

Fundamental Solutions to Pell's Equation


Note: This page uses MathML. To view it properly, you need a MathML-enabled browser. You may also have to install some fonts.


N = 2..1000

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
2 3 2 3 2 - 2 . 2 2 = 1
3 2 1 2 2 - 3 . 1 2 = 1
5 9 4 9 2 - 5 . 4 2 = 1
6 5 2 5 2 - 6 . 2 2 = 1
7 8 3 8 2 - 7 . 3 2 = 1
10 19 6 19 2 - 10 . 6 2 = 1
11 10 3 10 2 - 11 . 3 2 = 1
13 649 180 649 2 - 13 . 180 2 = 1
14 15 4 15 2 - 14 . 4 2 = 1
15 4 1 4 2 - 15 . 1 2 = 1
17 33 8 33 2 - 17 . 8 2 = 1
19 170 39 170 2 - 19 . 39 2 = 1
21 55 12 55 2 - 21 . 12 2 = 1
22 197 42 197 2 - 22 . 42 2 = 1
23 24 5 24 2 - 23 . 5 2 = 1
26 51 10 51 2 - 26 . 10 2 = 1
29 9801 1820 9801 2 - 29 . 1820 2 = 1
30 11 2 11 2 - 30 . 2 2 = 1
31 1520 273 1520 2 - 31 . 273 2 = 1
33 23 4 23 2 - 33 . 4 2 = 1
34 35 6 35 2 - 34 . 6 2 = 1
35 6 1 6 2 - 35 . 1 2 = 1
37 73 12 73 2 - 37 . 12 2 = 1
38 37 6 37 2 - 38 . 6 2 = 1
39 25 4 25 2 - 39 . 4 2 = 1
41 2049 320 2049 2 - 41 . 320 2 = 1
42 13 2 13 2 - 42 . 2 2 = 1
43 3482 531 3482 2 - 43 . 531 2 = 1
46 24335 3588 24335 2 - 46 . 3588 2 = 1
47 48 7 48 2 - 47 . 7 2 = 1
51 50 7 50 2 - 51 . 7 2 = 1
53 66249 9100 66249 2 - 53 . 9100 2 = 1
55 89 12 89 2 - 55 . 12 2 = 1
57 151 20 151 2 - 57 . 20 2 = 1
58 19603 2574 19603 2 - 58 . 2574 2 = 1
59 530 69 530 2 - 59 . 69 2 = 1
61 1766319049 226153980 1766319049 2 - 61 . 226153980 2 = 1
62 63 8 63 2 - 62 . 8 2 = 1
65 129 16 129 2 - 65 . 16 2 = 1
66 65 8 65 2 - 66 . 8 2 = 1
67 48842 5967 48842 2 - 67 . 5967 2 = 1
69 7775 936 7775 2 - 69 . 936 2 = 1
70 251 30 251 2 - 70 . 30 2 = 1
71 3480 413 3480 2 - 71 . 413 2 = 1
73 2281249 267000 2281249 2 - 73 . 267000 2 = 1
74 3699 430 3699 2 - 74 . 430 2 = 1
77 351 40 351 2 - 77 . 40 2 = 1
78 53 6 53 2 - 78 . 6 2 = 1
79 80 9 80 2 - 79 . 9 2 = 1
82 163 18 163 2 - 82 . 18 2 = 1
83 82 9 82 2 - 83 . 9 2 = 1
85 285769 30996 285769 2 - 85 . 30996 2 = 1
86 10405 1122 10405 2 - 86 . 1122 2 = 1
87 28 3 28 2 - 87 . 3 2 = 1
89 500001 53000 500001 2 - 89 . 53000 2 = 1
91 1574 165 1574 2 - 91 . 165 2 = 1
93 12151 1260 12151 2 - 93 . 1260 2 = 1
94 2143295 221064 2143295 2 - 94 . 221064 2 = 1
95 39 4 39 2 - 95 . 4 2 = 1
97 62809633 6377352 62809633 2 - 97 . 6377352 2 = 1
101 201 20 201 2 - 101 . 20 2 = 1
102 101 10 101 2 - 102 . 10 2 = 1
103 227528 22419 227528 2 - 103 . 22419 2 = 1
105 41 4 41 2 - 105 . 4 2 = 1
106 32080051 3115890 32080051 2 - 106 . 3115890 2 = 1
107 962 93 962 2 - 107 . 93 2 = 1
109 158070671986249 15140424455100 158070671986249 2 - 109 . 15140424455100 2 = 1
110 21 2 21 2 - 110 . 2 2 = 1
111 295 28 295 2 - 111 . 28 2 = 1
113 1204353 113296 1204353 2 - 113 . 113296 2 = 1
114 1025 96 1025 2 - 114 . 96 2 = 1
115 1126 105 1126 2 - 115 . 105 2 = 1
118 306917 28254 306917 2 - 118 . 28254 2 = 1
119 120 11 120 2 - 119 . 11 2 = 1
122 243 22 243 2 - 122 . 22 2 = 1
123 122 11 122 2 - 123 . 11 2 = 1
127 4730624 419775 4730624 2 - 127 . 419775 2 = 1
129 16855 1484 16855 2 - 129 . 1484 2 = 1
130 6499 570 6499 2 - 130 . 570 2 = 1
131 10610 927 10610 2 - 131 . 927 2 = 1
133 2588599 224460 2588599 2 - 133 . 224460 2 = 1
134 145925 12606 145925 2 - 134 . 12606 2 = 1
137 6083073 519712 6083073 2 - 137 . 519712 2 = 1
138 47 4 47 2 - 138 . 4 2 = 1
139 77563250 6578829 77563250 2 - 139 . 6578829 2 = 1
141 95 8 95 2 - 141 . 8 2 = 1
142 143 12 143 2 - 142 . 12 2 = 1
143 12 1 12 2 - 143 . 1 2 = 1
145 289 24 289 2 - 145 . 24 2 = 1
146 145 12 145 2 - 146 . 12 2 = 1
149 25801741449 2113761020 25801741449 2 - 149 . 2113761020 2 = 1
151 1728148040 140634693 1728148040 2 - 151 . 140634693 2 = 1
154 21295 1716 21295 2 - 154 . 1716 2 = 1
155 249 20 249 2 - 155 . 20 2 = 1
157 46698728731849 3726964292220 46698728731849 2 - 157 . 3726964292220 2 = 1
158 7743 616 7743 2 - 158 . 616 2 = 1
159 1324 105 1324 2 - 159 . 105 2 = 1
161 11775 928 11775 2 - 161 . 928 2 = 1
163 64080026 5019135 64080026 2 - 163 . 5019135 2 = 1
165 1079 84 1079 2 - 165 . 84 2 = 1
166 1700902565 132015642 1700902565 2 - 166 . 132015642 2 = 1
167 168 13 168 2 - 167 . 13 2 = 1
170 339 26 339 2 - 170 . 26 2 = 1
173 2499849 190060 2499849 2 - 173 . 190060 2 = 1
174 1451 110 1451 2 - 174 . 110 2 = 1
177 62423 4692 62423 2 - 177 . 4692 2 = 1
178 1601 120 1601 2 - 178 . 120 2 = 1
179 4190210 313191 4190210 2 - 179 . 313191 2 = 1
181 2469645423824185801 183567298683461940 2469645423824185801 2 - 181 . 183567298683461940 2 = 1
182 27 2 27 2 - 182 . 2 2 = 1
183 487 36 487 2 - 183 . 36 2 = 1
185 9249 680 9249 2 - 185 . 680 2 = 1
186 7501 550 7501 2 - 186 . 550 2 = 1
187 1682 123 1682 2 - 187 . 123 2 = 1
190 52021 3774 52021 2 - 190 . 3774 2 = 1
191 8994000 650783 8994000 2 - 191 . 650783 2 = 1
193 6224323426849 448036604040 6224323426849 2 - 193 . 448036604040 2 = 1
194 195 14 195 2 - 194 . 14 2 = 1
195 14 1 14 2 - 195 . 1 2 = 1
197 393 28 393 2 - 197 . 28 2 = 1
199 16266196520 1153080099 16266196520 2 - 199 . 1153080099 2 = 1
201 515095 36332 515095 2 - 201 . 36332 2 = 1
202 19731763 1388322 19731763 2 - 202 . 1388322 2 = 1
203 57 4 57 2 - 203 . 4 2 = 1
205 39689 2772 39689 2 - 205 . 2772 2 = 1
206 59535 4148 59535 2 - 206 . 4148 2 = 1
209 46551 3220 46551 2 - 209 . 3220 2 = 1
210 29 2 29 2 - 210 . 2 2 = 1
211 278354373650 19162705353 278354373650 2 - 211 . 19162705353 2 = 1
213 194399 13320 194399 2 - 213 . 13320 2 = 1
214 695359189925 47533775646 695359189925 2 - 214 . 47533775646 2 = 1
215 44 3 44 2 - 215 . 3 2 = 1
217 3844063 260952 3844063 2 - 217 . 260952 2 = 1
218 126003 8534 126003 2 - 218 . 8534 2 = 1
219 74 5 74 2 - 219 . 5 2 = 1
221 1665 112 1665 2 - 221 . 112 2 = 1
222 149 10 149 2 - 222 . 10 2 = 1
223 224 15 224 2 - 223 . 15 2 = 1
226 451 30 451 2 - 226 . 30 2 = 1
227 226 15 226 2 - 227 . 15 2 = 1
229 5848201 386460 5848201 2 - 229 . 386460 2 = 1
230 91 6 91 2 - 230 . 6 2 = 1
231 76 5 76 2 - 231 . 5 2 = 1
233 1072400673 70255304 1072400673 2 - 233 . 70255304 2 = 1
235 46 3 46 2 - 235 . 3 2 = 1
237 228151 14820 228151 2 - 237 . 14820 2 = 1
238 11663 756 11663 2 - 238 . 756 2 = 1
239 6195120 400729 6195120 2 - 239 . 400729 2 = 1
241 10085143557001249 649641205044600 10085143557001249 2 - 241 . 649641205044600 2 = 1
246 88805 5662 88805 2 - 246 . 5662 2 = 1
247 85292 5427 85292 2 - 247 . 5427 2 = 1
249 8553815 542076 8553815 2 - 249 . 542076 2 = 1
251 3674890 231957 3674890 2 - 251 . 231957 2 = 1
253 3222617399 202604220 3222617399 2 - 253 . 202604220 2 = 1
254 255 16 255 2 - 254 . 16 2 = 1
255 16 1 16 2 - 255 . 1 2 = 1
257 513 32 513 2 - 257 . 32 2 = 1
258 257 16 257 2 - 258 . 16 2 = 1
259 847225 52644 847225 2 - 259 . 52644 2 = 1
262 104980517 6485718 104980517 2 - 262 . 6485718 2 = 1
263 139128 8579 139128 2 - 263 . 8579 2 = 1
265 73738369 4529712 73738369 2 - 265 . 4529712 2 = 1
266 685 42 685 2 - 266 . 42 2 = 1
267 2402 147 2402 2 - 267 . 147 2 = 1
269 13449 820 13449 2 - 269 . 820 2 = 1
271 115974983600 7044978537 115974983600 2 - 271 . 7044978537 2 = 1
273 727 44 727 2 - 273 . 44 2 = 1
274 3959299 239190 3959299 2 - 274 . 239190 2 = 1
277 159150073798980475849 9562401173878027020 159150073798980475849 2 - 277 . 9562401173878027020 2 = 1
278 2501 150 2501 2 - 278 . 150 2 = 1
281 2262200630049 134951575480 2262200630049 2 - 281 . 134951575480 2 = 1
282 2351 140 2351 2 - 282 . 140 2 = 1
283 138274082 8219541 138274082 2 - 283 . 8219541 2 = 1
285 2431 144 2431 2 - 285 . 144 2 = 1
286 561835 33222 561835 2 - 286 . 33222 2 = 1
287 288 17 288 2 - 287 . 17 2 = 1
290 579 34 579 2 - 290 . 34 2 = 1
291 290 17 290 2 - 291 . 17 2 = 1
293 12320649 719780 12320649 2 - 293 . 719780 2 = 1
295 2024999 117900 2024999 2 - 295 . 117900 2 = 1
298 335473872499 19433479650 335473872499 2 - 298 . 19433479650 2 = 1
299 415 24 415 2 - 299 . 24 2 = 1
301 5883392537695 339113108232 5883392537695 2 - 301 . 339113108232 2 = 1
302 4276623 246092 4276623 2 - 302 . 246092 2 = 1
303 2524 145 2524 2 - 303 . 145 2 = 1
305 489 28 489 2 - 305 . 28 2 = 1
307 88529282 5052633 88529282 2 - 307 . 5052633 2 = 1
309 64202725495 3652365444 64202725495 2 - 309 . 3652365444 2 = 1
310 848719 48204 848719 2 - 310 . 48204 2 = 1
311 16883880 957397 16883880 2 - 311 . 957397 2 = 1
313 32188120829134849 1819380158564160 32188120829134849 2 - 313 . 1819380158564160 2 = 1
314 392499 22150 392499 2 - 314 . 22150 2 = 1
317 248678907849 13967198980 248678907849 2 - 317 . 13967198980 2 = 1
318 107 6 107 2 - 318 . 6 2 = 1
319 12901780 722361 12901780 2 - 319 . 722361 2 = 1
321 215 12 215 2 - 321 . 12 2 = 1
322 323 18 323 2 - 322 . 18 2 = 1
323 18 1 18 2 - 323 . 1 2 = 1
326 325 18 325 2 - 326 . 18 2 = 1
327 217 12 217 2 - 327 . 12 2 = 1
329 2376415 131016 2376415 2 - 329 . 131016 2 = 1
330 109 6 109 2 - 330 . 6 2 = 1
331 2785589801443970 153109862634573 2785589801443970 2 - 331 . 153109862634573 2 = 1
334 63804373719695 3491219999244 63804373719695 2 - 334 . 3491219999244 2 = 1
335 604 33 604 2 - 335 . 33 2 = 1
337 2063810353129713793 112422913565764752 2063810353129713793 2 - 337 . 112422913565764752 2 = 1
339 97970 5321 97970 2 - 339 . 5321 2 = 1
341 10626551 575460 10626551 2 - 341 . 575460 2 = 1
345 6761 364 6761 2 - 345 . 364 2 = 1
346 17299 930 17299 2 - 346 . 930 2 = 1
347 641602 34443 641602 2 - 347 . 34443 2 = 1
349 169648201 9081060 169648201 2 - 349 . 9081060 2 = 1
353 10157115393 540608704 10157115393 2 - 353 . 540608704 2 = 1
354 258065 13716 258065 2 - 354 . 13716 2 = 1
355 954809 50676 954809 2 - 355 . 50676 2 = 1
357 3401 180 3401 2 - 357 . 180 2 = 1
358 176579805797 9332532726 176579805797 2 - 358 . 9332532726 2 = 1
359 360 19 360 2 - 359 . 19 2 = 1
362 723 38 723 2 - 362 . 38 2 = 1
365 23915529 1251796 23915529 2 - 365 . 1251796 2 = 1
366 907925 47458 907925 2 - 366 . 47458 2 = 1
367 19019995568 992835687 19019995568 2 - 367 . 992835687 2 = 1
370 213859 11118 213859 2 - 370 . 11118 2 = 1
371 1695 88 1695 2 - 371 . 88 2 = 1
373 52387849 2712540 52387849 2 - 373 . 2712540 2 = 1
374 3365 174 3365 2 - 374 . 174 2 = 1
377 233 12 233 2 - 377 . 12 2 = 1
379 12941197220540690 664744650125541 12941197220540690 2 - 379 . 664744650125541 2 = 1
381 1015 52 1015 2 - 381 . 52 2 = 1
382 164998439999 8442054600 164998439999 2 - 382 . 8442054600 2 = 1
383 18768 959 18768 2 - 383 . 959 2 = 1
385 95831 4884 95831 2 - 385 . 4884 2 = 1
386 111555 5678 111555 2 - 386 . 5678 2 = 1
389 3287049 166660 3287049 2 - 389 . 166660 2 = 1
390 79 4 79 2 - 390 . 4 2 = 1
391 7338680 371133 7338680 2 - 391 . 371133 2 = 1
393 46437143 2342444 46437143 2 - 393 . 2342444 2 = 1
394 312086396361222451 15722685507826110 312086396361222451 2 - 394 . 15722685507826110 2 = 1
395 159 8 159 2 - 395 . 8 2 = 1
397 838721786045180184649 42094239791738433660 838721786045180184649 2 - 397 . 42094239791738433660 2 = 1
398 399 20 399 2 - 398 . 20 2 = 1
399 20 1 20 2 - 399 . 1 2 = 1
401 801 40 801 2 - 401 . 40 2 = 1
402 401 20 401 2 - 402 . 20 2 = 1
403 669878 33369 669878 2 - 403 . 33369 2 = 1
406 59468095 2951352 59468095 2 - 406 . 2951352 2 = 1
407 2663 132 2663 2 - 407 . 132 2 = 1
409 25052977273092427986049 1238789998647218582160 25052977273092427986049 2 - 409 . 1238789998647218582160 2 = 1
410 81 4 81 2 - 410 . 4 2 = 1
411 49730 2453 49730 2 - 411 . 2453 2 = 1
413 113399 5580 113399 2 - 413 . 5580 2 = 1
415 18412804 903849 18412804 2 - 415 . 903849 2 = 1
417 85322647 4178268 85322647 2 - 417 . 4178268 2 = 1
418 33857 1656 33857 2 - 418 . 1656 2 = 1
419 270174970 13198911 270174970 2 - 419 . 13198911 2 = 1
421 3879474045914926879468217167061449 189073995951839020880499780706260 3879474045914926879468217167061449 2 - 421 . 189073995951839020880499780706260 2 = 1
422 7022501 341850 7022501 2 - 422 . 341850 2 = 1
426 88751 4300 88751 2 - 426 . 4300 2 = 1
427 62 3 62 2 - 427 . 3 2 = 1
429 1524095 73584 1524095 2 - 429 . 73584 2 = 1
430 2862251 138030 2862251 2 - 430 . 138030 2 = 1
431 151560720 7300423 151560720 2 - 431 . 7300423 2 = 1
433 104564907854286695713 5025068784834899736 104564907854286695713 2 - 433 . 5025068784834899736 2 = 1
434 125 6 125 2 - 434 . 6 2 = 1
435 146 7 146 2 - 435 . 7 2 = 1
437 4599 220 4599 2 - 437 . 220 2 = 1
438 293 14 293 2 - 438 . 14 2 = 1
439 440 21 440 2 - 439 . 21 2 = 1
442 883 42 883 2 - 442 . 42 2 = 1
443 442 21 442 2 - 443 . 21 2 = 1
445 43468489 2060604 43468489 2 - 445 . 2060604 2 = 1
446 110166015 5216512 110166015 2 - 446 . 5216512 2 = 1
447 148 7 148 2 - 447 . 7 2 = 1
449 71798771299708449 3388393513402120 71798771299708449 2 - 449 . 3388393513402120 2 = 1
451 46471490 2188257 46471490 2 - 451 . 2188257 2 = 1
453 1653751 77700 1653751 2 - 453 . 77700 2 = 1
454 16916040084175685 793909098494766 16916040084175685 2 - 454 . 793909098494766 2 = 1
455 64 3 64 2 - 455 . 3 2 = 1
457 6983244756398928218113 326662411570389853632 6983244756398928218113 2 - 457 . 326662411570389853632 2 = 1
458 22899 1070 22899 2 - 458 . 1070 2 = 1
461 1182351890184201 55067617520620 1182351890184201 2 - 461 . 55067617520620 2 = 1
462 43 2 43 2 - 462 . 2 2 = 1
463 247512720456368 11502891625161 247512720456368 2 - 463 . 11502891625161 2 = 1
465 15871 736 15871 2 - 465 . 736 2 = 1
466 938319425 43466808 938319425 2 - 466 . 43466808 2 = 1
467 1625626 75225 1625626 2 - 467 . 75225 2 = 1
469 137215 6336 137215 2 - 469 . 6336 2 = 1
470 1691 78 1691 2 - 470 . 78 2 = 1
471 7838695 361188 7838695 2 - 471 . 361188 2 = 1
473 87 4 87 2 - 473 . 4 2 = 1
474 193549 8890 193549 2 - 474 . 8890 2 = 1
478 1617319577991743 73974475657896 1617319577991743 2 - 478 . 73974475657896 2 = 1
479 2989440 136591 2989440 2 - 479 . 136591 2 = 1
481 1859131879201 84769117080 1859131879201 2 - 481 . 84769117080 2 = 1
482 483 22 483 2 - 482 . 22 2 = 1
483 22 1 22 2 - 483 . 1 2 = 1
485 969 44 969 2 - 485 . 44 2 = 1
487 51906073840568 2352088722477 51906073840568 2 - 487 . 2352088722477 2 = 1
489 7592629975 343350596 7592629975 2 - 489 . 343350596 2 = 1
491 93628044170 4225374483 93628044170 2 - 491 . 4225374483 2 = 1
493 935662752649 42140131020 935662752649 2 - 493 . 42140131020 2 = 1
494 73035 3286 73035 2 - 494 . 3286 2 = 1
497 1201887 53912 1201887 2 - 497 . 53912 2 = 1
498 179777 8056 179777 2 - 498 . 8056 2 = 1
499 4490 201 4490 2 - 499 . 201 2 = 1
501 11242731902975 502288218432 11242731902975 2 - 501 . 502288218432 2 = 1
502 3832352837 171046278 3832352837 2 - 502 . 171046278 2 = 1
503 24648 1099 24648 2 - 503 . 1099 2 = 1
505 809 36 809 2 - 505 . 36 2 = 1
506 45 2 45 2 - 506 . 2 2 = 1
509 313201220822405001 13882400040814700 313201220822405001 2 - 509 . 13882400040814700 2 = 1
510 271 12 271 2 - 510 . 12 2 = 1
511 4188548960 185290497 4188548960 2 - 511 . 185290497 2 = 1
514 4625 204 4625 2 - 514 . 204 2 = 1
515 17406 767 17406 2 - 515 . 767 2 = 1
517 590968985399 25990786260 590968985399 2 - 517 . 25990786260 2 = 1
518 2367 104 2367 2 - 518 . 104 2 = 1
519 14851876 651925 14851876 2 - 519 . 651925 2 = 1
521 32961431500035201 1444066532654320 32961431500035201 2 - 521 . 1444066532654320 2 = 1
523 81810300626 3577314675 81810300626 2 - 523 . 3577314675 2 = 1
526 84056091546952933775 3665019757324295532 84056091546952933775 2 - 526 . 3665019757324295532 2 = 1
527 528 23 528 2 - 527 . 23 2 = 1
530 1059 46 1059 2 - 530 . 46 2 = 1
533 74859849 3242540 74859849 2 - 533 . 3242540 2 = 1
534 3678725 159194 3678725 2 - 534 . 159194 2 = 1
535 1618804 69987 1618804 2 - 535 . 69987 2 = 1
537 192349463 8300492 192349463 2 - 537 . 8300492 2 = 1
538 9536081203 411129654 9536081203 2 - 538 . 411129654 2 = 1
541 3707453360023867028800645599667005001 159395869721270110077187138775196900 3707453360023867028800645599667005001 2 - 541 . 159395869721270110077187138775196900 2 = 1
542 4293183 184408 4293183 2 - 542 . 184408 2 = 1
543 669337 28724 669337 2 - 543 . 28724 2 = 1
545 1961 84 1961 2 - 545 . 84 2 = 1
546 701 30 701 2 - 546 . 30 2 = 1
547 160177601264642 6848699678673 160177601264642 2 - 547 . 6848699678673 2 = 1
551 8380 357 8380 2 - 551 . 357 2 = 1
553 624635837407 26562217704 624635837407 2 - 553 . 26562217704 2 = 1
554 60756099699 2581279330 60756099699 2 - 554 . 2581279330 2 = 1
555 1814 77 1814 2 - 555 . 77 2 = 1
557 27849 1180 27849 2 - 557 . 1180 2 = 1
559 506568295 21425556 506568295 2 - 559 . 21425556 2 = 1
561 522785 22072 522785 2 - 561 . 22072 2 = 1
562 220938497 9319728 220938497 2 - 562 . 9319728 2 = 1
563 68122 2871 68122 2 - 563 . 2871 2 = 1
565 435259412378569 18311501103948 435259412378569 2 - 565 . 18311501103948 2 = 1
566 95609285 4018758 95609285 2 - 566 . 4018758 2 = 1
569 16760473211643448449 702635588524014320 16760473211643448449 2 - 569 . 702635588524014320 2 = 1
570 191 8 191 2 - 570 . 8 2 = 1
571 181124355061630786130 7579818350628982587 181124355061630786130 2 - 571 . 7579818350628982587 2 = 1
573 383 16 383 2 - 573 . 16 2 = 1
574 575 24 575 2 - 574 . 24 2 = 1
577 1153 48 1153 2 - 577 . 48 2 = 1
579 385 16 385 2 - 579 . 16 2 = 1
581 152071153975 6308974548 152071153975 2 - 581 . 6308974548 2 = 1
582 193 8 193 2 - 582 . 8 2 = 1
583 8429543 349116 8429543 2 - 583 . 349116 2 = 1
586 33867877212256207699 1399069112058008310 33867877212256207699 2 - 586 . 1399069112058008310 2 = 1
587 1907162 78717 1907162 2 - 587 . 78717 2 = 1
589 41423166067036218751 1706811823063746000 41423166067036218751 2 - 589 . 1706811823063746000 2 = 1
590 5781 238 5781 2 - 590 . 238 2 = 1
591 165676 6815 165676 2 - 591 . 6815 2 = 1
593 721517598849 29629176560 721517598849 2 - 593 . 29629176560 2 = 1
595 18514 759 18514 2 - 595 . 759 2 = 1
597 463287093751 18961078500 463287093751 2 - 597 . 18961078500 2 = 1
598 1574351 64380 1574351 2 - 598 . 64380 2 = 1
599 24686379794520 1008658133851 24686379794520 2 - 599 . 1008658133851 2 = 1
601 38902815462492318420311478049 1586878942101888360258625080 38902815462492318420311478049 2 - 601 . 1586878942101888360258625080 2 = 1
602 687 28 687 2 - 602 . 28 2 = 1
606 42187499 1713750 42187499 2 - 606 . 1713750 2 = 1
607 164076033968 6659640783 164076033968 2 - 607 . 6659640783 2 = 1
609 605695 24544 605695 2 - 609 . 24544 2 = 1
610 10323982819 418005846 10323982819 2 - 610 . 418005846 2 = 1
611 236926 9585 236926 2 - 611 . 9585 2 = 1
613 464018873584078278910994299849 18741545784831997880308784340 464018873584078278910994299849 2 - 613 . 18741545784831997880308784340 2 = 1
614 348291186245 14055888354 348291186245 2 - 614 . 14055888354 2 = 1
615 124 5 124 2 - 615 . 5 2 = 1
617 3363593612801313 135413180018248 3363593612801313 2 - 617 . 135413180018248 2 = 1
618 10093 406 10093 2 - 618 . 406 2 = 1
619 517213510553282930 20788566180548739 517213510553282930 2 - 619 . 20788566180548739 2 = 1
622 13804370063 553504812 13804370063 2 - 622 . 553504812 2 = 1
623 624 25 624 2 - 623 . 25 2 = 1
626 1251 50 1251 2 - 626 . 50 2 = 1
627 626 25 626 2 - 627 . 25 2 = 1
629 123245001 4914100 123245001 2 - 629 . 4914100 2 = 1
631 48961575312998650035560 1949129537575151036427 48961575312998650035560 2 - 631 . 1949129537575151036427 2 = 1
633 440772247 17519124 440772247 2 - 633 . 17519124 2 = 1
634 8711856945587257031251 345992039259400361250 8711856945587257031251 2 - 634 . 345992039259400361250 2 = 1
635 126 5 126 2 - 635 . 5 2 = 1
638 42283 1674 42283 2 - 638 . 1674 2 = 1
641 2609429220845977814049 103066257550962737720 2609429220845977814049 2 - 641 . 103066257550962737720 2 = 1
642 5777 228 5777 2 - 642 . 228 2 = 1
643 1988960193026 78436933185 1988960193026 2 - 643 . 78436933185 2 = 1
645 1024001 40320 1024001 2 - 645 . 40320 2 = 1
646 305 12 305 2 - 646 . 12 2 = 1
647 120187368 4725053 120187368 2 - 647 . 4725053 2 = 1
649 1123593226162199 44104892095380 1123593226162199 2 - 649 . 44104892095380 2 = 1
651 1735 68 1735 2 - 651 . 68 2 = 1
653 10499986568677299849 410896226494013260 10499986568677299849 2 - 653 . 410896226494013260 2 = 1
654 8915765 348634 8915765 2 - 654 . 348634 2 = 1
655 737709209 28824684 737709209 2 - 655 . 28824684 2 = 1
658 1693 66 1693 2 - 658 . 66 2 = 1
659 5930 231 5930 2 - 659 . 231 2 = 1
661 16421658242965910275055840472270471049 638728478116949861246791167518480580 16421658242965910275055840472270471049 2 - 661 . 638728478116949861246791167518480580 2 = 1
662 1718102501 66775950 1718102501 2 - 662 . 66775950 2 = 1
663 103 4 103 2 - 663 . 4 2 = 1
665 13719 532 13719 2 - 665 . 532 2 = 1
667 107119097 4147668 107119097 2 - 667 . 4147668 2 = 1
669 14226117859054135 550013492618436 14226117859054135 2 - 669 . 550013492618436 2 = 1
670 5791211 223734 5791211 2 - 670 . 223734 2 = 1
671 58620 2263 58620 2 - 671 . 2263 2 = 1
673 4765506835465395993032041249 183696788896587421699032600 4765506835465395993032041249 2 - 673 . 183696788896587421699032600 2 = 1
674 675 26 675 2 - 674 . 26 2 = 1
677 1353 52 1353 2 - 677 . 52 2 = 1
678 677 26 677 2 - 678 . 26 2 = 1
679 17792625320 682818291 17792625320 2 - 679 . 682818291 2 = 1
681 10743166003415 411679015748 10743166003415 2 - 681 . 411679015748 2 = 1
682 1197901 45870 1197901 2 - 682 . 45870 2 = 1
683 170067682 6507459 170067682 2 - 683 . 6507459 2 = 1
685 95592800063517769 3652413145693884 95592800063517769 2 - 685 . 3652413145693884 2 = 1
687 165337 6308 165337 2 - 687 . 6308 2 = 1
689 105 4 105 2 - 689 . 4 2 = 1
690 1471 56 1471 2 - 690 . 56 2 = 1
691 31138100617500578690 1184549173291009383 31138100617500578690 2 - 691 . 1184549173291009383 2 = 1
694 38782105445014642382885 1472148590903997672114 38782105445014642382885 2 - 694 . 1472148590903997672114 2 = 1
695 33639 1276 33639 2 - 695 . 1276 2 = 1
697 34849 1320 34849 2 - 697 . 1320 2 = 1
698 51999603 1968214 51999603 2 - 698 . 1968214 2 = 1
699 2271050 85899 2271050 2 - 699 . 85899 2 = 1
701 277631049 10485980 277631049 2 - 701 . 10485980 2 = 1
703 1159172 43719 1159172 2 - 703 . 43719 2 = 1
705 237161 8932 237161 2 - 705 . 8932 2 = 1
706 34595 1302 34595 2 - 706 . 1302 2 = 1
707 2526 95 2526 2 - 707 . 95 2 = 1
709 665782673992201 25003993164540 665782673992201 2 - 709 . 25003993164540 2 = 1
710 1279 48 1279 2 - 710 . 48 2 = 1
713 5286367 197976 5286367 2 - 713 . 197976 2 = 1
714 4115 154 4115 2 - 714 . 154 2 = 1
715 75646 2829 75646 2 - 715 . 2829 2 = 1
717 6998399 261360 6998399 2 - 717 . 261360 2 = 1
718 8933399183036079503 333391496474140716 8933399183036079503 2 - 718 . 333391496474140716 2 = 1
719 403480310400 15047276489 403480310400 2 - 719 . 15047276489 2 = 1
721 18632176943292415 693898530122112 18632176943292415 2 - 721 . 693898530122112 2 = 1
723 242 9 242 2 - 723 . 9 2 = 1
727 728 27 728 2 - 727 . 27 2 = 1
730 1459 54 1459 2 - 730 . 54 2 = 1
731 730 27 730 2 - 731 . 27 2 = 1
733 195307849 7213860 195307849 2 - 733 . 7213860 2 = 1
734 10394175 383656 10394175 2 - 734 . 383656 2 = 1
737 252975383 9318468 252975383 2 - 737 . 9318468 2 = 1
739 98015661073616742153890 3605564376516452758671 98015661073616742153890 2 - 739 . 3605564376516452758671 2 = 1
741 7352695 270108 7352695 2 - 741 . 270108 2 = 1
742 263091151 9658380 263091151 2 - 742 . 9658380 2 = 1
743 714024 26195 714024 2 - 743 . 26195 2 = 1
745 12769001 467820 12769001 2 - 745 . 467820 2 = 1
746 61268974069299 2243216519470 61268974069299 2 - 746 . 2243216519470 2 = 1
749 1084616384895 39631020176 1084616384895 2 - 749 . 39631020176 2 = 1
751 7293318466794882424418960 266136970677206024456793 7293318466794882424418960 2 - 751 . 266136970677206024456793 2 = 1
753 308526027863 11243313484 308526027863 2 - 753 . 11243313484 2 = 1
754 836977699 30480930 836977699 2 - 754 . 30480930 2 = 1
755 1209 44 1209 2 - 755 . 44 2 = 1
757 3750107388553 136299971388 3750107388553 2 - 757 . 136299971388 2 = 1
758 413959717 15035694 413959717 2 - 758 . 15035694 2 = 1
759 551 20 551 2 - 759 . 20 2 = 1
761 1280001 46400 1280001 2 - 761 . 46400 2 = 1
762 6349 230 6349 2 - 762 . 230 2 = 1
763 719724601 26055780 719724601 2 - 763 . 26055780 2 = 1
766 145933611945744638015 5272795728865625208 145933611945744638015 2 - 766 . 5272795728865625208 2 = 1
767 31212 1127 31212 2 - 767 . 1127 2 = 1
769 535781868388881310859702308423201 19320788325040337217824455505160 535781868388881310859702308423201 2 - 769 . 19320788325040337217824455505160 2 = 1
770 111 4 111 2 - 770 . 4 2 = 1
771 2989136930 107651137 2989136930 2 - 771 . 107651137 2 = 1
773 3607394696649 129748968980 3607394696649 2 - 773 . 129748968980 2 = 1
777 223 8 223 2 - 777 . 8 2 = 1
778 5964562960504723 213839942395674 5964562960504723 2 - 778 . 213839942395674 2 = 1
779 11785490 422259 11785490 2 - 779 . 422259 2 = 1
781 67606199 2419140 67606199 2 - 781 . 2419140 2 = 1
782 783 28 783 2 - 782 . 28 2 = 1
785 1569 56 1569 2 - 785 . 56 2 = 1
786 785 28 785 2 - 786 . 28 2 = 1
787 34625394242 1234262007 34625394242 2 - 787 . 1234262007 2 = 1
789 16116667272575 573768548496 16116667272575 2 - 789 . 573768548496 2 = 1
790 6616066879 235389096 6616066879 2 - 790 . 235389096 2 = 1
791 225 8 225 2 - 791 . 8 2 = 1
793 4393 156 4393 2 - 793 . 156 2 = 1
794 1828310451 64884310 1828310451 2 - 794 . 64884310 2 = 1
795 6626 235 6626 2 - 795 . 235 2 = 1
797 1221759532448649 43276943002540 1221759532448649 2 - 797 . 43276943002540 2 = 1
798 113 4 113 2 - 798 . 4 2 = 1
799 424 15 424 2 - 799 . 15 2 = 1
802 295496099 10434330 295496099 2 - 802 . 10434330 2 = 1
803 7226 255 7226 2 - 803 . 255 2 = 1
805 1514868641 53392104 1514868641 2 - 805 . 53392104 2 = 1
806 6166395 217202 6166395 2 - 806 . 217202 2 = 1
807 51841948 1824923 51841948 2 - 807 . 1824923 2 = 1
809 376455160998025676163201 13235458622462202510640 376455160998025676163201 2 - 809 . 13235458622462202510640 2 = 1
811 1382072163578616410 48531117622921197 1382072163578616410 2 - 811 . 48531117622921197 2 = 1
813 2167 76 2167 2 - 813 . 76 2 = 1
814 4206992174549 147454999410 4206992174549 2 - 814 . 147454999410 2 = 1
815 156644 5487 156644 2 - 815 . 5487 2 = 1
817 343 12 343 2 - 817 . 12 2 = 1
818 40899 1430 40899 2 - 818 . 1430 2 = 1
821 9000987377460935993101449 314136625452886403879740 9000987377460935993101449 2 - 821 . 314136625452886403879740 2 = 1
822 7397 258 7397 2 - 822 . 258 2 = 1
823 235170474903644006168 8197527430497636651 235170474903644006168 2 - 823 . 8197527430497636651 2 = 1
826 222239304685 7732694382 222239304685 2 - 826 . 7732694382 2 = 1
827 900602 31317 900602 2 - 827 . 31317 2 = 1
829 479835713751049 16665383182260 479835713751049 2 - 829 . 16665383182260 2 = 1
830 146411 5082 146411 2 - 830 . 5082 2 = 1
831 9799705 339948 9799705 2 - 831 . 339948 2 = 1
834 6552578705 226897244 6552578705 2 - 834 . 226897244 2 = 1
835 34336355806 1188258591 34336355806 2 - 835 . 1188258591 2 = 1
838 42112785797 1454762046 42112785797 2 - 838 . 1454762046 2 = 1
839 840 29 840 2 - 839 . 29 2 = 1
842 1683 58 1683 2 - 842 . 58 2 = 1
843 842 29 842 2 - 843 . 29 2 = 1
849 1501654712948695 51536656330476 1501654712948695 2 - 849 . 51536656330476 2 = 1
851 8418574 288585 8418574 2 - 851 . 288585 2 = 1
853 215454135724113414336120649 7377009103065498851032020 215454135724113414336120649 2 - 853 . 7377009103065498851032020 2 = 1
854 1294299 44290 1294299 2 - 854 . 44290 2 = 1
857 131822292741249 4502963741200 131822292741249 2 - 857 . 4502963741200 2 = 1
858 703 24 703 2 - 858 . 24 2 = 1
859 2058844771979643060124010 70246877103894937291269 2058844771979643060124010 2 - 859 . 70246877103894937291269 2 = 1
861 541601801 18457740 541601801 2 - 861 . 18457740 2 = 1
862 358022566147312125503 12194296994921665128 358022566147312125503 2 - 862 . 12194296994921665128 2 = 1
863 18524026608 630565199 18524026608 2 - 863 . 630565199 2 = 1
865 242688628535063329 8251660923733224 242688628535063329 2 - 865 . 8251660923733224 2 = 1
866 42435 1442 42435 2 - 866 . 1442 2 = 1
869 60192738698751 2041898807200 60192738698751 2 - 869 . 2041898807200 2 = 1
870 59 2 59 2 - 870 . 2 2 = 1
871 19442812076 658794555 19442812076 2 - 871 . 658794555 2 = 1
874 3725 126 3725 2 - 874 . 126 2 = 1
877 116476476553 3933131148 116476476553 2 - 877 . 3933131148 2 = 1
878 9314703 314356 9314703 2 - 878 . 314356 2 = 1
879 107245324 3617295 107245324 2 - 879 . 3617295 2 = 1
881 22606256615916825861249 761624136944072910800 22606256615916825861249 2 - 881 . 761624136944072910800 2 = 1
883 34878475759617272473442 1173754162936357802169 34878475759617272473442 2 - 883 . 1173754162936357802169 2 = 1
885 119 4 119 2 - 885 . 4 2 = 1
886 7743524593057655851637765 260148796464024194850378 7743524593057655851637765 2 - 886 . 260148796464024194850378 2 = 1
887 469224 15755 469224 2 - 887 . 15755 2 = 1
889 13231974717803657215 443786188413453504 13231974717803657215 2 - 889 . 443786188413453504 2 = 1
890 179 6 179 2 - 890 . 6 2 = 1
893 6091434999 203842100 6091434999 2 - 893 . 203842100 2 = 1
894 299 10 299 2 - 894 . 10 2 = 1
895 359 12 359 2 - 895 . 12 2 = 1
897 599 20 599 2 - 897 . 20 2 = 1
898 899 30 899 2 - 898 . 30 2 = 1
899 30 1 30 2 - 899 . 1 2 = 1
901 1801 60 1801 2 - 901 . 60 2 = 1
902 901 30 901 2 - 902 . 30 2 = 1
903 601 20 601 2 - 903 . 20 2 = 1
905 361 12 361 2 - 905 . 12 2 = 1
906 301 10 301 2 - 906 . 10 2 = 1
907 123823410343073497682 4111488857741309517 123823410343073497682 2 - 907 . 4111488857741309517 2 = 1
910 181 6 181 2 - 910 . 6 2 = 1
911 371832584927520 12319363142953 371832584927520 2 - 911 . 12319363142953 2 = 1
913 515734243080407 17068312251564 515734243080407 2 - 913 . 17068312251564 2 = 1
914 62563299 2069410 62563299 2 - 914 . 2069410 2 = 1
915 121 4 121 2 - 915 . 4 2 = 1
917 823604599 27197820 823604599 2 - 917 . 27197820 2 = 1
919 4481603010937119451551263720 147834442396536759781499589 4481603010937119451551263720 2 - 919 . 147834442396536759781499589 2 = 1
921 2522057712835735 83104627139412 2522057712835735 2 - 921 . 83104627139412 2 = 1
922 351605368773852499 11579506138834350 351605368773852499 2 - 922 . 11579506138834350 2 = 1
923 638 21 638 2 - 923 . 21 2 = 1
926 304560297142335 10008472361032 304560297142335 2 - 926 . 10008472361032 2 = 1
929 13224937103288377430049 433896111669844912840 13224937103288377430049 2 - 929 . 433896111669844912840 2 = 1
930 61 2 61 2 - 930 . 2 2 = 1
933 75263 2464 75263 2 - 933 . 2464 2 = 1
934 3034565 99294 3034565 2 - 934 . 99294 2 = 1
935 1376 45 1376 2 - 935 . 45 2 = 1
937 480644425002415999597113107233 15701968936415353889062192632 480644425002415999597113107233 2 - 937 . 15701968936415353889062192632 2 = 1
938 17151 560 17151 2 - 938 . 560 2 = 1
939 122695 4004 122695 2 - 939 . 4004 2 = 1
941 1068924905989944201 34845956052079180 1068924905989944201 2 - 941 . 34845956052079180 2 = 1
942 106133 3458 106133 2 - 942 . 3458 2 = 1
943 737 24 737 2 - 943 . 24 2 = 1
946 45225786400145 1470417148788 45225786400145 2 - 946 . 1470417148788 2 = 1
947 13509645362 439004487 13509645362 2 - 947 . 439004487 2 = 1
949 609622436806639069525576201 19789181711517243032971740 609622436806639069525576201 2 - 949 . 19789181711517243032971740 2 = 1
951 224208076 7270445 224208076 2 - 951 . 7270445 2 = 1
953 15090531843660371073 488830275367615376 15090531843660371073 2 - 953 . 488830275367615376 2 = 1
955 2095256249 67800900 2095256249 2 - 955 . 67800900 2 = 1
957 14849 480 14849 2 - 957 . 480 2 = 1
958 16762522330425599 541572514048560 16762522330425599 2 - 958 . 541572514048560 2 = 1
959 960 31 960 2 - 959 . 31 2 = 1
962 1923 62 1923 2 - 962 . 62 2 = 1
965 446526729 14374204 446526729 2 - 965 . 14374204 2 = 1
966 57499 1850 57499 2 - 966 . 1850 2 = 1
967 4649532557817485528 149518887194649693 4649532557817485528 2 - 967 . 149518887194649693 2 = 1
969 13588951 436540 13588951 2 - 969 . 436540 2 = 1
970 215395035859 6915917802 215395035859 2 - 970 . 6915917802 2 = 1
971 12479806786330 400496058813 12479806786330 2 - 971 . 400496058813 2 = 1
973 903223 28956 903223 2 - 973 . 28956 2 = 1
974 488825745235215 15662987185124 488825745235215 2 - 974 . 15662987185124 2 = 1
977 108832847723078562849 3481871275306470280 108832847723078562849 2 - 977 . 3481871275306470280 2 = 1
978 118337 3784 118337 2 - 978 . 3784 2 = 1
979 360449 11520 360449 2 - 979 . 11520 2 = 1
982 8837 282 8837 2 - 982 . 282 2 = 1
983 284088 9061 284088 2 - 983 . 9061 2 = 1
985 332929 10608 332929 2 - 985 . 10608 2 = 1
986 49299 1570 49299 2 - 986 . 1570 2 = 1
987 377 12 377 2 - 987 . 12 2 = 1
989 550271588560695 17497618534396 550271588560695 2 - 989 . 17497618534396 2 = 1
991 379516400906811930638014896080 12055735790331359447442538767 379516400906811930638014896080 2 - 991 . 12055735790331359447442538767 2 = 1
993 2647 84 2647 2 - 993 . 84 2 = 1
994 1135 36 1135 2 - 994 . 36 2 = 1
995 8835999 280120 8835999 2 - 995 . 280120 2 = 1
997 14418057673 456624468 14418057673 2 - 997 . 456624468 2 = 1
998 984076901 31150410 984076901 2 - 998 . 31150410 2 = 1

J.P. Martin-Flatin