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Diophantine Equations

Science > Math > Number Theory > Diophantine Equations

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Equal Sums of Like Powers (9)
Fermat's Last Theorem (18)

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	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.
	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.
	Bibliography on Hilbert's Tenth Problem - http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html Searchable, 400 items.
	Linear Diophantine Equations - http://www.thoralf.uwaterloo.ca/htdocs/linear.html A web tool for solving Diophantine equations of the form ax + by = c.

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

	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.
	Diophantine Geometry in Characteristic p - http://www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.html A survey by José Felipe Voloch.
	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.hbmeyer.de/pythagen.htm A Javascript calculator for pythagorean triplets.
	Diagonal Quartic Surfaces - http://www.boojum.org.uk/maths/quartic-surfaces/ Articles, computations and software in Magma and GP by Martin Bright.

	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.
	Pell's Equation - http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch8_6.html Provides information on this equation, solved by Brahmagupta in 628 AD.

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