Directory of Diophantine Equations Resources

Home > Science > Math > Number Theory > Diophantine Equations

In this category are included any equation or set of equations where the unknowns must be integer numbers. It includes Fermat Last Theorem as a special case.

Subcategories

• Equal Sums of Like Powers
• Fermat's Last Theorem

Resources in This Category

• Bibliography on Hilbert's Tenth Problem

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

• Diagonal Quartic Surfaces

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

• 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.

• 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.

• 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.

• Linear Diophantine Equations

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

• 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.

• Pell's Equation

  http://sweet.ua.pt/tos/pell.html
  Record solutions.

• 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.

• 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.

• 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.

• 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.

• 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.

Other Languages

• Spanish

 

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