Number Theory
- 44
- Hilbert's Tenth Problem
- Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
- 45
- Hilbert's Tenth Problem
- Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers.
- 47
- Pythagorean Triples in JAVA
- A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
- 49
- Quadratic Diophantine Equation Solver
- Dario Alpern's Java/JavaScript code that solves Diophantine equations of the form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 in two selectable modes: "solution only" and "step by step" (or "teach") mode. There is also a link to his description of the solving methods.
- 50
- Thue Equations
- Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
- 51
- A Proof of the Full Shimura-Taniyama-Weil Conjecture
- Article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor. [PDF]
- 52
- Algorithms for Modular Elliptic Curves
- Book by John Cremona, with introduction, tables and software.
- 54
- Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory
- Compiled by Paul Garrett, 1996.
- 55
- Counting Points on Elliptic Curves
- Robert Harley, Pierrick Gaudry, François Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm by to Takakazu Satoh.
- 56
- ECDL Project
- Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.
- 57
- ECMNET
- The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.