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Science: Math: Number_Theory: Diophantine_Equations

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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 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.

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.

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
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.

Pell's Equation
Record solutions.

Pythagorean Triples Etcetera
A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles.

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 and Integral Points on Higher-dimensional Varieties
Some of conjectures and open problems, compiled at AIM.

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.

Thue Equations
Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.


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