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Centuries of crop diversity are at risk of being lost forever as farmers turn to just a few modern, high yielding varieties.

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Beagle hunter

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Venomous mammal caught on camera

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Mosquitoes make sweet love music

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Mummy of female pharaoh uncovered

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Tech fair offers greener vision

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Everest trip helps critically ill

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Panda bites his third tourist in two years at Beijing zoo

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Zimbabwe troops 'eat elephants'

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Our writers talk back

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Holes give edge to new armour

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First flight of algae-fuelled jet

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China alert over bird flu death

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Body repair 'could be ramped up'

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US vows 'huge' marine protection

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Feilden's blog

Ground-breaking new technique in stem cell science

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Heat may spark world food crisis

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Baby Jupiter's huge weight gain

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Canadians claim South Pole record

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 Science > Math > Number Theory > Diophantine Equations

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Science > Math > Number Theory > Diophantine Equations

Diophantine Equations:

Bibliography on Hilbert's Tenth Problem

Searchable, 400 items.

http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html

Graand

Free Classified Ads Portal

www.graand.com

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.HTM

Diagonal Quartic Surfaces

Articles, computations and software in Magma and GP by Martin Bright.

http://www.boojum.org.uk/maths/quartic-surfaces/

Diophantine Equations

A survey by José Felipe Voloch.

http://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.

http://www.math.hr/~duje/dtuples.html

Diophantus Quadraticus

On-line Pell Equation solver by Michael Zuker.

http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html

Egyptian Fractions

Lots of information about Egyptian fractions collected by David Eppstein.

http://www.ics.uci.edu/~eppstein/numth/egypt/

The Erdos-Strauss Conjecture

The page establishes that the conjecture is true for all integers. Tables and software by Allan Swett.

http://math.uindy.edu/swett/esc.htm

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/

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

Linear Diophantine Equations

A web tool for solving Diophantine equations of the form ax + by = c.

http://www.thoralf.uwaterloo.ca/htdocs/linear.html

Pell's Equation

Record solutions.

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

Pythagorean Triples Etcetera

A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles.

http://www.geocities.com/fredlb37/

Pythagorean Triples in JAVA

A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.

http://www.hbnweb.de/pythagoras/pythagoras.html

Pythagorean Triplets

A Javascript calculator for pythagorean triplets.

http://www.hbmeyer.de/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.

http://www.alpertron.com.ar/QUAD.HTM

Rational and Integral Points on Higher-dimensional Varieties

Some of conjectures and open problems, compiled at AIM.

http://aimath.org/WWN/qptsurface2/

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.html

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/thue.html