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Topia!: Science: Math: Number Theory: Diophantine Equations (51)
Bibliography on Hilbert's Tenth Problem - Searchable, ~400 items. Diophantine Equations - Dave Rusin's guide to Diophantine equations. 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. Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Methods to solve these equations. Thue Equations - Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger. Hilbert's Tenth Problem - Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites. Diophantine Geometry in Characteristic p - A survey by José Felipe Voloch. Pythagorean Triplets - A Javascript calculator for pythagorean triplets. 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. 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. Pythagorean Triples in JAVA - A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2. 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. Rational Triangles - Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples. On the Psixyology of Diophantine Equations - PhD thesis, Pieter Moree, Leiden, 1993. Solving General Pell Equations - John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N. Pell's Equation - Record solutions. Fermat's Method of Infinite Descent - Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4. Diophantus Quadraticus - On-line Pell Equation solver by Michael Zuker. Rational and Integral Points on Higher-dimensional Varieties - Some of conjectures and open problems, compiled at AIM.
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