Science » Math » Number Theory » Diophantine Equations (index): Bibliography on Hilbert's Tenth Problem, Egyptian Fractions, The Erdos-Strauss Conjecture, Thue Equations ...


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08 November, 2009

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Bibliography on Hilbert's Tenth Problem (Popularity:

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http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html
Searchable, ~400 items.

Egyptian Fractions (Popularity:

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

The Erdos-Strauss Conjecture (Popularity:

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http://math.uindy.edu/swett/esc.htm
The conjecture states that for any integer n > 1 there are integers a, b, and c with 4/n = ...

Thue Equations (Popularity:

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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.

Hilbert's Tenth Problem (Popularity:

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

Diophantine Geometry in Characteristic p (Popularity:

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http://www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.html
A survey by José Felipe Voloch.

Pythagorean Triplets (Popularity:

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

Hilbert's Tenth Problem (Popularity:

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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 ...

Quadratic Diophantine Equation Solver (Popularity:

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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 ...

Pythagorean Triples in JAVA (Popularity:

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http://home.foni.net/~heinzbecker/pythagoras.html
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.

Diophantine m-tuples (Popularity:

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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 ...

Rational Triangles (Popularity:

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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 (Popularity:

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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.

Pell's Equation (Popularity:

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http://www.ieeta.pt/~tos/pell.html
Record solutions.

Diophantus Quadraticus (Popularity:

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

Rational and Integral Points on Higher-dimensional Varieties (Popularity:

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http://aimath.org/WWN/qptsurface2/
Some of conjectures and open problems, compiled at AIM.

Diagonal Quartic Surfaces (Popularity:

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

Linear Diophantine Equations (Popularity:

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

Tom's Mathematical Things (Popularity:

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http://tom.womack.net/maths/dissert_abstract.htm
Dissertation about equal sums of like powers by Tom Womack.

Power Page (Popularity:

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http://www.uwgb.edu/dutchs/RECMATH/rmpowers.htm
Steve Dutch's page about powers of numbers.