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 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.
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. Help build the largest human-edited directory on the web.