Katolog > Science > Math > Number Theory > 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.

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Equal Sums of Like Powers (10) Fermat's Last Theorem (19)

Links:

Fermat's Method of Infinite Descent Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4. sweb.uky.edu/~jrbail01/fermat.htm

Diophantine Equations Dave Rusin's guide to Diophantine equations. www.math.niu.edu/~rusin/papers/known-math/index/11DXX.html

Egyptian Fractions Lots of information about Egyptian fractions collected by David Eppstein. www.ics.uci.edu/~eppstein/numth/egypt

Bibliography on Hilbert's Tenth Problem Searchable, ~400 items. liinwww.ira.uka.de/bibliography/Math/Hilbert10.html

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. 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. finanz.math.tu-graz.ac.at/~cheub/thue.html

Hilbert's Tenth Problem Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites. logic.pdmi.ras.ru/Hilbert10

Diophantine Geometry in Characteristic p A survey by José Felipe Voloch. www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.html

Pythagorean Triplets A Javascript calculator for pythagorean triplets. 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. 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 description of the solving met 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. 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. 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. 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. hometown.aol.com/jpr2718/pelleqns.html

Pell's Equation Record solutions. www.ieeta.pt/~tos/pell.html

Diophantus Quadraticus On-line Pell Equation solver by Michael Zuker. www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html

Rational and Integral Points on Higher-dimensional Varieties Some of conjectures and open problems, compiled at AIM. aimath.org/WWN/qptsurface2

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. www.math.leidenuniv.nl/~tengely/main2.html

Diagonal Quartic Surfaces Articles, computations and software in Magma and GP by Martin Bright. www.boojum.org.uk/maths/quartic-surfaces

Linear Diophantine Equations A web tool for solving Diophantine equations of the form ax + by = c. www.thoralf.uwaterloo.ca/htdocs/linear.html

Pythagorean Triples Etcetera A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles. www.geocities.com/fredlb37