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Diophantine Equations
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> Equal Sums of Like Powers
> Fermat's Last Theorem


Bibliography on Hilbert's Tenth Problem open in new window
Searchable, ~400 items.
(http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html)

Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n open in new window
Methods to solve these equations.
(http://www.biochem.okstate.edu/OAS/OJAS/thiendo.htm)

Diophantine Equations open in new window
Dave Rusin's guide to Diophantine equations.
(http://www.math.niu.edu/~rusin/papers/known-math/index/11DXX)

Diophantine Geometry in Characteristic p open in new window
A survey by José Felipe Voloch.
(http://www.ma.utexas.edu/users/voloch/surveylatex/surveylate)

Diophantine m-tuples open in new window
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)

Diophantus Quadraticus open in new window
On-line Pell Equation solver by Michael Zuker.
(http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html)

Egyptian Fractions open in new window
Lots of information about Egyptian fractions collected by David Eppstein.
(http://www.ics.uci.edu/~eppstein/numth/egypt/)

Fermat's Method of Infinite Descent open in new window
Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.
(http://sweb.uky.edu/~jrbail01/fermat.htm)

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

Hilbert's Tenth Problem open in new window
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)

Linear Diophantine Equations open in new window
A web tool for solving Diophantine equations of the form ax + by = c.
(http://thoralf2.uwaterloo.ca/htdocs/linear.html)

On the Psixyology of Diophantine Equations open in new window
PhD thesis, Pieter Moree, Leiden, 1993.
(http://web.inter.NL.net/hcc/J.Moree/linkind2.htm)

Pell's Equation open in new window
Record solutions.
(http://www.ieeta.pt/~tos/pell.html)

Pythagorean Triples in JAVA open in new window
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
(http://home.foni.net/~heinzbecker/pythagoras.html)

Pythagorean Triplets open in new window
A Javascript calculator for pythagorean triplets.
(http://www.faust.fr.bw.schule.de/mhb/pythagen.htm)

Quadratic Diophantine Equation Solver open in new window
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.
(http://www.alpertron.com.ar/QUAD.HTM)

Rational and Integral Points on Higher-dimensional Varieties open in new window
Some of conjectures and open problems, compiled at AIM.
(http://aimath.org/WWN/qptsurface2/)

Rational Triangles open in new window
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 open in new window
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)

The Erdos-Strauss Conjecture open in new window
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.
(http://math.uindy.edu/swett/esc.htm)

Thue Equations open in new window
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)


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