Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16: Fermat the integer set 1, 3, 8, 120.

Searchable, ~400 items.

Methods to solve these equations.

Dave Rusin's guide to Diophantine equations.

A survey by José Felipe Voloch.

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

On-line Pell Equation solver by Michael Zuker.

Lots of information about Egyptian fractions collected by David Eppstein.

Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.

Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.

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.

A web tool for solving Diophantine equations of the form ax + by = c.

PhD thesis, Pieter Moree, Leiden, 1993.

Record solutions.

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

A Javascript calculator for pythagorean triplets.

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

Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.

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

The conjecture states that for any integer n > 1 there are integers a, b, and c with 4/n = 1/a + 1/b + 1/c, a > 0, b > 0, c > 0. The page establishes that the conjecture is true for all integers n, 1 < n <= 10^14. Tables and softwar