Top : Science : Math : Number Theory : Diophantine Equations

    Web site listings: [ Hide summaries ]
    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.
    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.
    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.
    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
    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 softwar
    Thue Equations 
    Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.