Diophantine Equations Number Theory Math

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.

• Diophantus Quadraticus - On-line Pell Equation solver by Michael Zuker.
  
• Linear Diophantine Equations - A web tool for solving Diophantine equations of the form ax + by = c.
  
• Pell's Equation - Provides information on this equation, solved by Brahmagupta in 628 AD.
  
• Pythagorean Triplets - A Javascript calculator for pythagorean triplets.
  
• Rational and Integral Points on Higher-dimensional Varieties - Some of conjectures and open problems, compiled at AIM.
  
• Pythagorean Triples Etcetera - A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles.
  
• The Erdos-Strauss Conjecture - The page establishes that the conjecture is true for all integers. Tables and software by Allan Swett.
  
• Diophantine Geometry in Characteristic p - A survey by José Felipe Voloch.
  
• Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Methods to solve these equations.
  
• Diagonal Quartic Surfaces - Articles, computations and software in Magma and GP by Martin Bright.
  
• Rational Triangles - Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
  
• 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
  
• Pythagorean Triples in JAVA - A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
  
• 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.
  
• Egyptian Fractions - Lots of information about Egyptian fractions collected by David Eppstein.
  
• 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.
  
• Thue Equations - Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
  
• Bibliography on Hilbert's Tenth Problem - Searchable, 400 items.
  
  

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