Diophantine Equations
Dave Rusin's guide to Diophantine equations.
http://www.math.niu.edu/~rusin/papers/known-math/index/11DXX.html
Egyptian Fractions
Lots of information about Egyptian fractions collected by David Eppstein.
http://www.ics.uci.edu/~eppstein/numth/egypt/
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
http://math.uindy.edu/swett/esc.htm
Thue Equations
Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
http://finanz.math.tu-graz.ac.at/~cheub/thue.html
Pythagorean Triplets
A Javascript calculator for pythagorean triplets.
http://www.faust.fr.bw.schule.de/mhb/pythagen.htm
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.
http://www.ltn.lv/~podnieks/gt4.html
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
http://www.alpertron.com.ar/QUAD.HTM
Pythagorean Triples in JAVA
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
http://home.foni.net/~heinzbecker/pythagoras.html
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.
http://www.math.hr/~duje/dtuples.html
Rational Triangles
Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
http://grail.cba.csuohio.edu/~somos/rattri.html
Solving General Pell Equations
John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
http://hometown.aol.com/jpr2718/pelleqns.html
Pell's Equation
Record solutions.
http://www.ieeta.pt/~tos/pell.html
Fermat's Method of Infinite Descent
Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.
http://sweb.uky.edu/~jrbail01/fermat.htm
Diophantus Quadraticus
On-line Pell Equation solver by Michael Zuker.
http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html
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.
http://www.weburbia.demon.co.uk/pg/diophant.htm
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.
http://www.math.leidenuniv.nl/~tengely/main2.html
Diagonal Quartic Surfaces
Articles, computations and software in Magma and GP by Martin Bright.
http://www.boojum.org.uk/maths/quartic-surfaces/
Linear Diophantine Equations
A web tool for solving Diophantine equations of the form ax + by = c.
http://www.thoralf.uwaterloo.ca/htdocs/linear.html
Last Updated: 2005-02-03 22:53:58
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