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- 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.
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
- Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
Hilbert's Tenth Problem
- Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
Keith Numbers
- A recreational mathematics problem related to recurrent sequences and Diophantine equations.
Linear Diophantine Equations
- A web tool for solving Diophantine equations of the form ax + by = c.
Links on Diophantine m-tuples
- Sets of rational numbers such that the product of any two is one less than a square. Maintained by Andrej Dujella, Zagreb.
Lower Bounds for Solving Linear Diophantine Equations on Random Access Machines
- Abstract: a lower bound for the complexity of solving linear Diophantine equations such as knapsack problems on an idealised computer.
On the Psixyology of Diophantine Equations
- PhD thesis, Pieter Moree, Leiden, 1993.
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.
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.
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