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Home / Science / Math / Number Theory / Diophantine Equations
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- 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.
www.weburbia.com/pg/diophant.htm
- Bibliography on Hilbert's Tenth Problem - Searchable, ~400 items.
liinwww.ira.uka.de/bibliography/Math/Hilbert10.html
- Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Methods to solve these equations.
www.biochem.okstate.edu/OAS/OJAS/thiendo.htm
- Diophantine Equations - Dave Rusin's guide to Diophantine equations.
www.math.niu.edu/~rusin/papers/known-math/index/11DXX.html
- Diophantine Geometry in Characteristic p - A survey by José Felipe Voloch.
www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.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
- Diophantus Quadraticus - On-line Pell Equation solver by Michael Zuker.
www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html
- Egyptian Fractions - Lots of information about Egyptian fractions collected by David Eppstein.
www.ics.uci.edu/~eppstein/numth/egypt
- 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
- 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
- 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
- Linear Diophantine Equations - A web tool for solving Diophantine equations of the form ax + by = c.
thoralf2.uwaterloo.ca/htdocs/linear.html
- On the Psixyology of Diophantine Equations - PhD thesis, Pieter Moree, Leiden, 1993.
web.inter.NL.net/hcc/J.Moree/linkind2.htm
- Pell's Equation - Record solutions.
www.ieeta.pt/~tos/pell.html
- 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
- Pythagorean Triplets - A Javascript calculator for pythagorean triplets.
www.faust.fr.bw.schule.de/mhb/pythagen.htm
- 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 methods.
www.alpertron.com.ar/QUAD.HTM
- 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
- 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
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