Surf these sites: 1, 3, 8, 120, ... -- The Greek mathematician Diophantus was born circa the year 200 AD in Alexandria. He is best known for his work to solve indeterminate equations in rational numbers. One of the puzzles he set was to find sets of unequal fractions such that the product of any two is one less than a square. We don''t know why he picked this problem but it certainly turns out to be an interesting one. One such set of four which he found was, 1/16, 33/16, 17/4, 105/16 Fermat also looked at Diophantine''s problem but he was more interested in whole number solutions than fractions. He found, 1, 3, 8, 120 Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n -- Methods to solve these equations. Diophantine equations -- Dave Rusin''s guide to Diophantine equations. Diophantine geometry in characteristic p -- A survey by José Felipe Voloch Diophantus Quadraticus -- Calculator that solves Pell Equations, i.e. Diophantine Equations of the form: X^2 - dY^2 = (+/-)1. Egyptian Fractions -- Lots of information about Egyptian fractions collected by David Eppstein. 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. Hilbert''s Tenth Problem -- Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites. Keith Numbers -- A recreational mathematics problem related with generalized Fibonacci sequences and Diophantine equations Linear Diophantine Equations -- A web tool for solving Diophantine equations of the form ax + by = c. Lower bounds for solving linear diophantine equations on random access machines. -- A random access machine is an abstract device, which is convenient for estimating complexity of computations. 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. Thue equations -- Definition of the problem and a list of special cases that have been solved.
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