Diophantine Equations

Bibliography on Hilbert's Tenth Problem :

- Searchable, 400 items.
Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n :

- Methods to solve these equations.
Diagonal Quartic Surfaces :

- Articles, computations and software in Magma and GP by Martin Bright.
Diophantine Geometry in Characteristic p :

- A survey by José Felipe Voloch.
Diophantine m-tuples :

- Sets with the property that the product of any two distinct elements is one less than a square. Notes and bibliography by Andrej Dujella.
Diophantus Quadraticus :

- On-line Pell Equation solver by Michael Zuker.
Egyptian Fractions :

- Lots of information about Egyptian fractions collected by David Eppstein.
The Erdos-Strauss Conjecture :

- The page establishes that the conjecture is true for all integers. Tables and software by Allan Swett.
Hilbert's Tenth Problem :

- Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
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.
Linear Diophantine Equations :

- A web tool for solving Diophantine equations of the form ax + by = c.
Pell's Equation :

- Record solutions.
Pythagorean Triples Etcetera :

- A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles.
Pythagorean Triples in JAVA :

- A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
Pythagorean Triplets :

- A Javascript calculator for pythagorean triplets.
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.
Rational and Integral Points on Higher-dimensional Varieties :

- Some of conjectures and open problems, compiled at AIM.
Rational Triangles :

- Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
Solving General Pell Equations :

- John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
Thue Equations :

- Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.