Diophantine Equations

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» 1, 3, 8, 120, ... - 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.
» 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.
» Diophantine Equations - Dave Rusin's guide to Diophantine equations.
» 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.
» Fermat's Method of Infinite Descent - Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.
» 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.
» On the Psixyology of Diophantine Equations - PhD thesis, Pieter Moree, Leiden, 1993.
» Pell's Equation - Record solutions.
» 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
» Rational Triangles - Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
» Rational and Integral Points on Higher-dimensional Varieties - Some of conjectures and open problems, compiled at AIM.
» Solving General Pell Equations - John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
» The Erdos-Strauss Conjecture - 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
» Thue Equations - Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.