Diophantine Equations Number Theory Math

Diophantine Equations Number Theory Math

Diophantine Equations

In this category are included any equation or set of equations where the unknowns must be integer numbers. It includes Fermat Last Theorem as a special case.

Top: Science: Math: Number Theory: Diophantine Equations

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

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