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Top > Science > Math > Number Theory > Diophantine Equations 


Bibliography on Hilbert's Tenth Problem  Searchable, ~400 items. Diophantine Equations  Dave Rusin's guide to Diophantine equations. Lower Bounds for Solving Linear Diophantine Equations on Random Access Machines  Abstract: a lower bound for the complexity of solving linear Diophantine equations such as knapsack problems on an idealised computer. Egyptian Fractions  Lots of information about Egyptian fractions collected by David Eppstein. The ErdosStrauss 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. 1, 3, 8, 120, ...  Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16: Fermat the integer set 1, 3, 8, 120. Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n  Methods to solve these equations. Keith Numbers  A recreational mathematics problem related to recurrent sequences and Diophantine equations. Thue Equations  Definition of the problem and a list of special cases that have been solved. 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 JosÃ© Felipe Voloch. Fermat's Method of Infinite Descent  Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4. Pythagorean Triplets  A Javascript calculator for pythagorean triplets. Links on Diophantine mtuples  Sets of rational numbers such that the product of any two is one less than a square. Maintained by Andrej Dujella, Zagreb. 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 mtuples  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.

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