Diophantine Equations

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.

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

Some of conjectures and open problems, compiled at AIM.

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

NOVA Online presents The Proof, including an interview with Andrew Wiles, an essay on Sophie Germain, and the Pythagorean theorem.

Article in Eric Weisstein's World of Mathematics.