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Search Home : Science : Math : Number Theory : Diophantine Equations
- 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.
- Diagonal Quartic Surfaces: Articles, computations and software in Magma and GP by Martin Bright.
- 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.
- Hilbert's Tenth Problem: Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
- Linear Diophantine Equations: A web tool for solving Diophantine equations of the form ax + by = c.
- MAGMA program: MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied. Created by Szabolcs Tengely.
- 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 description of the solving methods.
- 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 Allan Swett.
- Thue Equations: Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
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