Bazsites.com Diophantine Equations
Directory Topics
On the Web
- Linear Diophantine Equations - A web tool for solving Diophantine equations of the form ax + by = c.
- 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.
- Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Methods to solve these equations.
- Solving General Pell Equations - John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
- 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.
- The Beal Conjecture - $75,000 prized problem pertaining to the Diophantine equation of the form A^x + B^y = C^z where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common factor.
- Equations Involving Sums of Powers - Joseph McLean's investigations into those equations.
- Ziegler, Volker - TU Graz. Diophantine equations, especially Thue equations. Publications.
- 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.
- Equal Sums of Like Powers - Chen Shuwen's extensive collection of equal sums of like powers, especially those that are solutions to multigrade equations.
Wikipedia Articles
- Diophantine equation - In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations.
- Glossary of arithmetic and Diophantine geometry - This is a glossary of arithmetic and Diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.
- Citrabhanu - Citrabanu(1530) a mathematician from the Kerala school in the 16th century mathematician from Kerala who gave integer solutions to 21 types of systems of two simultaneous Diophantine equations in two unknowns. These types are all the possible pairs of equations of the following seven forms:
- Archimedes' cattle problem - Archimedes' cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes, the problem involves computing the number of cattle in a herd of the sun god from a given set of restrictions.
- Aryabhata algorithm - Aryabhata algorithm is an algorithm to solve indeterminate Diophantine equations and for residue arithmetic. It is first described in the mathematician-astronomer Aryabhata's book Aryabhatiya (499).