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In this category are included any equation or set of equations where the unknowns must be integer numbers. It includes Fermat Last Theorem as a special case.

Equal Sums of Like Powers	Fermat's Last Theorem

• 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.
• Egyptian Fractions Egyptian mathematical fractions, including algorithms, transcriptions of network conversations, and links to other Egyptian mathematical resources.
• 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 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.
• 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 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.
• 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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