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Diophantine Equations

Science > Math > Number Theory > Diophantine Equations

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Equal Sums of Like Powers (8)
Fermat's Last Theorem (15)

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

Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - http://oas.ucok.edu/OJAS/98/T98/THIENDO.HTM
Methods to solve these equations.

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

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

Diophantine m-tuples - http://www.math.hr/~duje/dtuples.html
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 - http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html
On-line Pell Equation solver by Michael Zuker.

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

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

Hilbert's Tenth Problem - http://www.ltn.lv/~podnieks/gt4.html
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 - http://www.thoralf.uwaterloo.ca/htdocs/linear.html
A web tool for solving Diophantine equations of the form ax + by = c.

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

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

Pythagorean Triples in JAVA - http://www.hbnweb.de/pythagoras/pythagoras.html
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.

Pythagorean Triplets - http://www.faust.fr.bw.schule.de/mhb/pythagen.htm
A Javascript calculator for pythagorean triplets.

Quadratic Diophantine Equation Solver - http://www.alpertron.com.ar/QUAD.HTM
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 - http://aimath.org/WWN/qptsurface2/
Some of conjectures and open problems, compiled at AIM.

Rational Triangles - http://grail.cba.csuohio.edu/~somos/rattri.html
Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.

Solving General Pell Equations - http://hometown.aol.com/jpr2718/pelleqns.html
John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.

The Erdos-Strauss Conjecture - http://math.uindy.edu/swett/esc.htm
The page establishes that the conjecture is true for all integers. Tables and software by Allan Swett.

Thue Equations - http://finanz.math.tu-graz.ac.at/~cheub/thue.html
Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.

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