Geometry.Net - Math_Discover: Diophantine Equation

Dario Alpern's Generic Two Integer Variable 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
Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks
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

Extractions: Hilbert tenth problem, Diophantine equation, Hilbert, tenth problem, Matiyasevich, Robinson, Julia, 10th, problem, Davis, Martin, Diophantine, equation Back to title page Left Adjust your browser window Right Statement of the problem: 10. Determining the solvability of a Diophantine equation. 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. (See the original statement in German at http://logic.pdmi.ras.ru/Hilbert10/stat/stat.html Linear Diophantine equations Problems that can be solved by finding solutions of algebraic equations in the domain of integer numbers are known since the very beginning of mathematics. Some of these equations do not have solutions at all. For example, the equation 2x-2y=1 cannot have solutions in the domain of integer numbers since its left-hand side is always an even number. Some other equations have a finite set of solutions. For example, the equation 3x=6 has only one solution x=2. And finally, some equations have an infinite set of integer solutions. For example, let us solve the equation 7x-17y=1:
Diophantine Equation -- From MathWorld
Ogilvy and Anderson (1988) give a number of diophantine equations with known and A linear diophantine equation (in two variables) is an equation of the
http://mathworld.wolfram.com/DiophantineEquation.html

Extractions: MATHWORLD - IN PRINT Order book from Amazon Number Theory Diophantine Equations Diophantine Equation A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution. Such an algorithm does exist for the solution of first-order Diophantine equations. However, the impossibility of obtaining a general solution was proven by Yuri Matiyasevich in 1970 (Matiyasevich 1970, Davis 1973, Davis and Hersh 1973, Davis 1982, Matiyasevich 1993) by showing that the relation (where is the th Fibonacci number ) is Diophantine. More specifically, Matiyasevich showed that there is a polynomial in , and a number of other variables , ... having the property that iff there exist integers , ... such that
11D Diophantine Equations
(Thus the diophantine equation x^2+y^2=N can be treated both in 11P and here in 11D (as a Pell equation).)
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Diophantine Equation--3rd Powers -- From MathWorld
Thue showed that a diophantine equation of the form Miller, JCP and Woollett,MFC Solutions of the diophantine equation x^3+y^3+z^3k .
http://mathworld.wolfram.com/DiophantineEquation3rdPowers.html

Extractions: MATHWORLD - IN PRINT Order book from Amazon Number Theory Diophantine Equations Diophantine Equation3rd Powers As a part of the study of Waring's problem , it is known that every positive integer is a sum of no more than 9 positive cubes ( ), that every "sufficiently large" integer is a sum of no more than 7 positive cubes ( ; although it is not known if 7 can be reduced), and that every integer is a sum of at most 5 signed cubes ( ; although it is not known if 5 can be reduced to 4). It is known that every can be written is the form An elliptic curve of the form for an integer is known as a Mordell curve The 3.1.2 equation is a case of Fermat's last theorem with . In fact, this particular case was known not to have any solutions long before the general validity of Fermat's last theorem was established. Thue showed that a Diophantine equation of the form for , and integers, has only finite many solutions (Hardy 1999, pp. 78-79).
LINEAR DIOPHANTINE EQUATIONS
A web tool for solving diophantine equations of the form ax + by = c.
http://www.thoralf.uwaterloo.ca/htdocs/linear.html
Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks
Given a diophantine equation with any number of unknowns and with rational integer coefficients devise a process, which could determine by a finite
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
11D: Diophantine Equations
diophantine equations whose solution set is onedimensional are discussed withalgebraic Some diophantine equations are best thought of as part of 11J
http://www.math.niu.edu/~rusin/known-math/index/11DXX.html

Extractions: POINTERS: Texts Software Web links Selected topics here See also 11GXX, 14GXX. In particular, discussion of many examples and families of equations has been moved to pages for (arithmetic) algebraic geometry; the dividing line is unclear sorry. Diophantine equations whose solution set is one-dimensional are discussed with algebraic curves . This includes single equations in 2 variables (or homogeneous equations in 3 variables, such as the Fermat equation). In particular,... Equations whose solutions are curves of genus 1 are discussed in the subsection on elliptic curves . Examples include cubics in two variables, homogeneous cubics in three variables, pairs of quadratics in four variables, and equations of the form y^2=Q(x) where Q is a polynomial of degree 3 or 4. Sets of N equations in N+2 variables (or N+3 variables, if those equations are homogeneous) describe algebraic surfaces ; for example the question of the existence of a "rational box" is there.
Announce.html
International conference on diophantine equations in honour of Professor T.N. Shorey on his 60th Birthday. TIFR, Mumbai, India; 1620 December 2005.
http://www.math.tifr.res.in/~dion2005/
Clemens Heuberger - Thue Equations
any given polynomial diophantine equation; the negative answer has been given by Matijasevic in 1970. So the research interest in diophantine
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PhD Thesis
Thomas Stoll, TU Graz, 2003. Text (PS).
http://www.dmg.tuwien.ac.at/stoll/thesis.html
LINEAR DIOPHANTINE EQUATIONS
A web tool for solving diophantine equations of the form ax + by = c.
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Diophantine Equation - Wikipedia, The Free Encyclopedia
A linear diophantine equation is an equation between two sums of monomials of The depth of the study of general diophantine equations is shown by the
http://en.wikipedia.org/wiki/Diophantine_equation

Extractions: In mathematics , a Diophantine equation is a polynomial equation that only allows the variables to be integers . Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. The word Diophantine refers to the Greek mathematician of the third century A.D., Diophantus of Alexandria , who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra . The mathematical study of Diophantine problems Diophantus initiated is now called Diophantine analysis. A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. edit ax by = 1: See BÃ©zout's identity ; this is a linear Diophantine. x n y n z n : For n = 2 there are infinitely many solutions ( x y z ), the Pythagorean triples . For larger values of n Fermat's last theorem states that no positive integer solutions x y z satisfying the above equation exist.
Wakabayashi's Home Page
Seikei University, Tokyo. diophantine equations and transcendence problems for values of analytic functions.
http://www.ge.seikei.ac.jp/wakaba/

Extractions: áÑ÷Ìz[y[WÖæ¤±» Wakabayashi Isao's Home Page English ZF§180-8633 @@@s ìsgËk¬@3-3-1 @@@¬æüåwHw Address: Department of Engineering, Seikei University, @@@@@Kichijoji Kitamachi 3, Musashino-shi, @@@@@Tokyo 180-8633, Japan E-mail: wakaba@ plus ge.seikei.ac.jp (óÆplusðæÁÄlßÄº³¢j @@@@@@@@@@@@@@@@@@@@@@iPlease take off " plus ".) Tel.@: 0422-37-3808 (Office) ±Ì v¤±Æ í½µÌSÈÚ my research
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
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Category:Diophantine Equations - Wikipedia, The Free Encyclopedia
For more information, see the article about diophantine equations. This categoryroughly corresponds to MSC 11D diophantine equations
http://en.wikipedia.org/wiki/Category:Diophantine_equations

Extractions: This category roughly corresponds to MSC 11D Diophantine equations There is 1 subcategory to this category. There are 11 articles in this category. Retrieved from " http://en.wikipedia.org/wiki/Category:Diophantine_equations Categories Number theory Equations Views Personal tools Navigation Search Toolbox In other languages This page was last modified 14:33, 25 July 2005. All text is available under the terms of the GNU Free Documentation License (see for details).
Hilbert Tenth Problem Database Index
Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126
Math Forum - Ask Dr. Math Archives: Diophantine Equations
diophantine equations, a selection of answers from the Dr. Math archives.diophantine equations We have searched the Web for information about Diophantine
http://mathforum.org/library/drmath/sets/select/dm_diophantine.html
Solving General Pell Equations
John Robertson's treatise on how to solve diophantine equations of the form x^2 dy^2 = N.
http://hometown.aol.com/jpr2718/pelleqns.html
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
http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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