Searchable, ~400 items.
Dave Rusin's guide to Diophantine equations.
Lots of information about Egyptian fractions collected by David Eppstein.
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 software by Allan Swett.
Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
A survey by José Felipe Voloch.
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.