Lukol Directory: Science: Math: Number Theory: Diophantine Equations

Rational Triangles 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... Solving General Pell Equations John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N. http://hometown.aol.com/jpr2718/pelleqns.h... Rational and Integral Points on Higher-dimensional Varieties Some of conjectures and open problems, compiled at AIM. http://aimath.org/WWN/qptsurface2/ Thue Equations 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/th... Pythagorean Triples in JAVA A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2. http://home.foni.net/~heinzbecker/pythagor... 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. http://www.alpertron.com.ar/QUAD.HTM Diophantus Quadraticus On-line Pell Equation solver by Michael Zuker. http://www.bioinfo.rpi.edu/~zukerm/cgi-bin... Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n Methods to solve these equations. http://oas.ucok.edu/OJAS/98/T98/THIENDO.HT... Pythagorean Triples Etcetera A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles. http://www.geocities.com/fredlb37/ Diagonal Quartic Surfaces Articles, computations and software in Magma and GP by Martin Bright. http://www.boojum.org.uk/maths/quartic-sur... 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. http://www.math.hr/~duje/dtuples.html 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. http://www.ltn.lv/~podnieks/gt4.html Hilbert's Tenth Problem Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites. http://logic.pdmi.ras.ru/Hilbert10/ Linear Diophantine Equations A web tool for solving Diophantine equations of the form ax + by = c. http://www.thoralf.uwaterloo.ca/htdocs/lin... Pell's Equation Record solutions. http://www.ieeta.pt/~tos/pell.html Diophantine Geometry in Characteristic p A survey by José Felipe Voloch. http://www.ma.utexas.edu/users/voloch/surv... Egyptian Fractions Egyptian mathematical fractions, including algorithms, transcriptions of network conversations, and links to other Egyptian mathematical resources. http://www.ics.uci.edu/~eppstein/numth/egy... Bibliography on Hilbert's Tenth Problem Searchable, ~400 items. http://liinwww.ira.uka.de/bibliography/Mat... 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. http://math.uindy.edu/swett/esc.htm Diophantine Equations Dave Rusin's guide to Diophantine equations. http://www.math.niu.edu/~rusin/papers/know... Pythagorean Triplets A Javascript calculator for pythagorean triplets. http://www.faust.fr.bw.schule.de/mhb/pytha... Sub Topics: Equal Sums of Like Powers Fermat's Last Theorem

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2006