1. 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

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2. 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

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 4. Hilbert's Tenth Problem 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 4.1. History of the Problem. Story of the Solution 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:

3. 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

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team 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

4. 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

5. 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

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team 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).

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

Solving ax +by = c a b c

7. 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

8. 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

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 11D: Diophantine equations Introduction History Applications and related fields 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.

9. 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/

Stone by stone a wall is built, And each stone must lie square, Little by little a rose unfolds, And each petal must be fair, Little by little an idea is built, And day by day it grows, Stronger at last than a wall of stone and lovelier than a rose DION 2005 An International Conference on DIOPHANTINE EQUATIONS in honour of Professor T.N. Shorey on his 60th Birthday Venue TATA INSTITUTE OF FUNDAMENTAL RESEARCH Mumbai India. Read more about Mumbai City. Dates December 16, 2005 to December 20, 2005. Organising Committee: Dipendra Prasad, R. Parimala, A. Sankaranarayanan, N. Saradha, T.N. Venkataramana Speakers From Outside India M.A. Bennett ( University of British Columbia, Canada) Y. Bugeaud ( Universit Louis Pasteur, France) F. Luca (Instituto de Matematicas UNAM, Mexico) M. Mignotte (Universit Louis Pasteur, France) Yu. Nesterenko (Moscow State University, Russia) M. Nori (University of Chicago, USA) Noriko-Hirata Kohno (Nihon University, Japan) M. Ram Murty (Queen's University, Canada) A. Schinzel (Warszawa, Poland) W.M. Schmidt (University of Colorado at Boulder, USA)

10. 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 http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. PhD Thesis Thomas Stoll, TU Graz, 2003. Text (PS). http://www.dmg.tuwien.ac.at/stoll/thesis.html

PhD Thesis Finiteness results for Diophantine equations for polynomial families (Stoll Thomas) ( ps We study the general Diophantine equation A P_m(x)+ B P_n(y)=C in integers x, y, where A, B, C are fixed rational numbers and P_m(x) PhD thesis advisor: Tichy Robert, Dr.phil., O.Univ.-Prof. organization: Working Group Mathematics A of the Institute of Mathematics year of publication: Last modified: November 22, 2003

12. 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

13. 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

Diophantine equation From Wikipedia, the free encyclopedia. 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. Contents Examples of Diophantine equations Diophantine analysis Traditional questions Hilbert's tenth problem ... edit Examples of Diophantine equations ax by = 1: See B©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.

14. Wakabayashi's Home Page Seikei University, Tokyo. diophantine equations and transcendence problems for values of analytic functions. http://www.ge.seikei.ac.jp/wakaba/

Žá—ÑŒ÷‚̃z[ƒ€ƒy[ƒW‚ւ悤‚±‚» Wakabayashi Isao's Home Page English ZŠF§180-8633 @@@“Œ‹ž“s•‘ –ìŽs‹gËŽ›–k’¬@3-3-1 @@@¬æü‘åŠwHŠw•” Address: Department of Engineering, Seikei University, @@@@@Kichijoji Kitamachi 3, Musashino-shi, @@@@@Tokyo 180-8633, Japan E-mail: wakaba@ plus ge.seikei.ac.jp (‹ó”’‚Æplus‚ðŽæ‚Á‚Ä‹l‚߂ĉº‚³‚¢j @@@@@@@@@@@@@@@@@@@@@@iPlease take off " plus ".) Tel.@: 0422-37-3808 (Office) ‚±‚̍ Žv‚¤‚±‚Æ ‚킽‚µ‚Ì’S“–‰È–Ú my research

15. 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

16. 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

Category:Diophantine equations From Wikipedia, the free encyclopedia. For more information, see the article about Diophantine equations This category roughly corresponds to MSC 11D Diophantine equations Subcategories There is 1 subcategory to this category. D Diophantine geometry Articles in category "Diophantine equations" There are 11 articles in this category. Diophantine equation B B©zout's identity C Catalan's conjecture D Diophantine set E Euler brick H Hasse principle I Infinite descent M Matiyasevich's theorem P Pell's equation Pythagorean triple T Thue equation Retrieved from " http://en.wikipedia.org/wiki/Category:Diophantine_equations Categories Number theory Equations Views Category Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link 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).

17. 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

18. 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

Ask Dr. Math Diophantine Equations Dr. Math Home Elementary Middle School High School ... Dr. Math FAQ Diophantine Equations , a selection of answers from the Dr. Math archives. Diophantine Equations We have searched the Web for information about Diophantine equations. Diophantine Equations, Step by Step Find all positive integer solutions to 43x + 7y + 17z = 400. Integer Solutions of ax + by = c Given the equation 5y - 3x = 1, how can I find solution points where x and y are both integers? Also, how can I show that there will always be integer points (x,y) in ax + by = c if a, b and c are all integers? Buying Cows, Pigs, and Chickens A farmer buys 100 animals for $100. The animals include at least one cow, one pig, and one chicken. If a cow costs $10, a pig costs $3, and a chicken costs $0.50, how many of each did he buy? How Many Mice, Cats, and Dogs? You must spend $100 to buy 100 pets, choosing at least one of each pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00 each, and dogs @ $15.00 each. How many mice, cats, and dogs must you buy? Money Puzzle A man goes to the bank and asks for x dollars and y cents.

19. 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

htmlAdWH('93212816', '728', '90'); Main Math Solving the generalized Pell equation x - Dy =N John Robertson An improved version of what used to be here is now a PDF file at my homepage . Look for the PDF file titled ``Solving the generalized Pell equation.'' The old HTML page (uncorrected, un-enhanced, on some browsers some math symbols do not display correctly) is at old HTML page. This page is best viewed using Microsoft Internet Explorer (MS IE). Last Modified August 3, 2002 John P. Robertson JPR2718@AOL.COM This page has been visited times.

20. 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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