Diophantine Equations Number Theory Math

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Top: Science: Math: Number_Theory: Diophantine_Equations:

• - Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
  
• - A web tool for solving Diophantine equations of the form ax + by = c.
  
• - 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.
  
• - PhD thesis, Pieter Moree, Leiden, 1993.
  
• - A Javascript calculator for pythagorean triplets.
  
• - 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
  
• - A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
  
• - Methods to solve these equations.
  
• - Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
  
• - MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied. Created by Szabolcs Tengely.
  
• - Searchable, ~400 items.
  
• - Record solutions.
  
• - Lots of information about Egyptian fractions collected by David Eppstein.
  
• - John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
  
• - 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
  
• - On-line Pell Equation solver by Michael Zuker.
  
• - A survey by José Felipe Voloch.
  
• - Sets with the property that the product of any two distinct elements is one less than a square. Notes and bibliography by Andrej Dujella.
  
• - Some of conjectures and open problems, compiled at AIM.
  
• - Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.
  
• - Dave Rusin's guide to Diophantine equations.
  
• - Articles, computations and software in Magma and GP by Martin Bright.