I have a passion for numbers and symbolic calculations. Since my teenage years, I have been interested in recreational mathematics, mathematical puzzles, fundamental properties of numbers (number theory), series, polynomials, and integrals. Here is a list of topics that kept me busy for a while. For some of them, the outcome of my calculations is available in XHTML/MathJax or XHTML/MathML format by clicking on the topic (some of these pages are huge and may take a long time to download).

General Topic | Especially... |
---|---|

Bernoulli numbers | |

Carmichael numbers | |

Chebyshev polynomials | |

Congruent numbers | |

Continued fractions | Continued fraction expansions of square roots |

Diophantine equations | Pell's equation |

Eight queens puzzle | Amazons on NxN chessboard |

Euclidean algorithm | |

Euler's totient function | |

Feigenbaum constants | |

Fermat's little theorem | |

Fractals | Mandelbrot set, Julia set |

Game of life | |

Generating functions | |

Graphs | |

Integrals | Indefinite integrals, Abelian integrals |

Legendre polynomials | |

Magic squares | |

Ordinary differential equations | Canonical ODEs |

Overhanging dominoes | |

Pi decimals | |

Polynomial congruences | |

Polynomial division | |

Polynomial interpolation | Cotesian numbers |

Polynomial recurrences | |

Prime numbers | Large primes, Mersenne primes, Prime factors |

Primitive roots modulo n | |

Quadratic residues | |

Riemann zeta function ζ(s) | |

Series | Power series, Taylor series, Maclaurin series, Laurent series, Formal power series, Closed-form expressions |

Sums of powers | Faulhaber's formula |

Tiling puzzles | Squared squares |

Trigonometric identities | Multiple-angle formulas: sin(2a), sin(3a), sin(4a), etc. |