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Top: Science: Math: Number Theory: Diophantine Equations (42)

Equal Sums of Like Powers (8)
Fermat's Last Theorem (15)

Sites:

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 page establishes that the conjecture is true for all integers. 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.

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