 |
/ Home
/ Web Directory / Science / Math / Number Theory / Diophantine Equations (57)
Sub-Categories in Diophantine Equations
Web Sites in Category Diophantine Equations
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.
Bibliography on Hilbert's Tenth Problem - Searchable, ~400 items.
Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Methods to solve these equations.
Diagonal Quartic Surfaces - Articles, computations and software in Magma and GP by Martin Bright.
Diophantine Equations - Dave Rusin's guide to Diophantine equations.
Diophantine Geometry in Characteristic p - A survey by José Felipe Voloch.
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.
MAGMA program - MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied. Created by Szabolcs Tengely.
On the Psixyology of Diophantine Equations - PhD thesis, Pieter Moree, Leiden, 1993.
Pell's Equation - Record solutions.
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 his description of the solving methods.
Rational and Integral Points on Higher-dimensional Varieties - Some of conjectures and open problems, compiled at AIM.
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 software by Allan Swett.
Thue Equations - Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
|
|
|
|
