Diophantine Equations (Number Theory)

Diophantine Equations further on these related pages:

Equal Sums of Like Powers Fermat's Last Theorem

Diophantine Equations Sites:

Diophantine m-tuples 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. (Diophantine Equations) http://www.math.hr/~duje/dtuples.html Pythagorean Triplets Pythagorean Triplets: A Javascript calculator for pythagorean triplets. (Diophantine Equations) http://www.faust.fr.bw.schule.de/mhb/pythagen.htm On the Psixyology of Diophantine Equations On the Psixyology of Diophantine Equations: PhD thesis, Pieter Moree, Leiden, 1993. (Diophantine Equations) http://web.inter.NL.net/hcc/J.Moree/linkind2.htm Bibliography on Hilbert's Tenth Problem Bibliography on Hilbert's Tenth Problem: Searchable, ~400 items. (Diophantine Equations) http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html Pell's Equation Pell's Equation: Record solutions. (Diophantine Equations) http://www.ieeta.pt/~tos/pell.html Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n: Methods to solve these equations. (Diophantine Equations) http://www.biochem.okstate.edu/OAS/OJAS/thiendo.htm Hilbert's Tenth Problem 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. (Diophantine Equations) http://www.ltn.lv/~podnieks/gt4.html Thue Equations Thue Equations: Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger. (Diophantine Equations) http://finanz.math.tu-graz.ac.at/~cheub/thue.html Quadratic Diophantine Equation Solver 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 (Diophantine Equations) http://www.alpertron.com.ar/QUAD.HTM Solving General Pell Equations Solving General Pell Equations: John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N. (Diophantine Equations) http://hometown.aol.com/jpr2718/pelleqns.html Egyptian Fractions Egyptian Fractions: Lots of information about Egyptian fractions collected by David Eppstein. (Diophantine Equations) http://www.ics.uci.edu/~eppstein/numth/egypt/ Diophantus Quadraticus Diophantus Quadraticus: On-line Pell Equation solver by Michael Zuker. (Diophantine Equations) http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html Linear Diophantine Equations Linear Diophantine Equations: A web tool for solving Diophantine equations of the form ax + by = c. (Diophantine Equations) http://thoralf2.uwaterloo.ca/htdocs/linear.html Pythagorean Triples in JAVA Pythagorean Triples in JAVA: A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2. (Diophantine Equations) http://home.foni.net/~heinzbecker/pythagoras.html Rational and Integral Points on Higher-dimensional Varieties Rational and Integral Points on Higher-dimensional Varieties: Some of conjectures and open problems, compiled at AIM. (Diophantine Equations) http://aimath.org/WWN/qptsurface2/ 1, 3, 8, 120, ... 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 Equations) http://www.weburbia.demon.co.uk/pg/diophant.htm Diophantine Geometry in Characteristic p Diophantine Geometry in Characteristic p: A survey by José Felipe Voloch. (Diophantine Equations) http://www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.html MAGMA program 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. (Diophantine Equations) http://www.math.leidenuniv.nl/~tengely/main2.html Diagonal Quartic Surfaces Diagonal Quartic Surfaces: Articles, computations and software in Magma and GP by Martin Bright. (Diophantine Equations) http://www.boojum.org.uk/maths/quartic-surfaces/ Fermat's Method of Infinite Descent Fermat's Method of Infinite Descent: Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4. (Diophantine Equations) http://sweb.uky.edu/~jrbail01/fermat.htm Diophantine Equations Diophantine Equations: Dave Rusin's guide to Diophantine equations. (Diophantine Equations) http://www.math.niu.edu/~rusin/papers/known-math/index/11DXX.html Rational Triangles Rational Triangles: Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples. (Diophantine Equations) http://grail.cba.csuohio.edu/~somos/rattri.html The Erdos-Strauss Conjecture 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 (Diophantine Equations) http://math.uindy.edu/swett/esc.htm