1. Diophantine Equation - Wikipedia, The Free Encyclopedia From MathWorld at Wolfram Research. Diophantine Equation. From PlanetMath. Retrieved from http//en.wikipedia.org/wiki/diophantine_equation http://en.wikipedia.org/wiki/Diophantine_equation

Diophantine equation From Wikipedia, the free encyclopedia Jump to: navigation search 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. In more technical language, they define an algebraic curve algebraic surface or more general object, and ask about the lattice points on it. The word Diophantine refers to the Hellenistic mathematician of the 3rd century, 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. While individual equations present a kind of puzzle and have been considered throughout history, the formulation of general theories of Diophantine equations (further to the theory of quadratic forms ) was an achievement of the twentieth century.

2. Diophantine Equation An equation that has integer coefficients and for which integer solutions are required. Such equations are named after Diophantus. http://www.daviddarling.info/encyclopedia/D/Diophantine_equation.html

NUMBER THEORY A B C ... CONTACT entire Web this site Diophantine equation An equation that has integer coefficients and for which integer solutions are required. Such equations are named after Diophantus . The best known examples are those from Pythagoras's theorem, a b c , when a b , and c Pythagorean triplet . Despite their simple appearance Diophantine equations can be fantastically difficult to solve. A notorious example comes from Fermat's last theorem (recently solved), a n b n c n for n To give a specific example, suppose we want to find integer values for x and y such that x y A trial and error approach using a computer would quickly find the solution: y x = 161. However, just a slight change to the equation to make it x y would leave the trial and error method floundering, even with the resources of the most powerful computers on Earth. The smallest integer solution to this innocent looking formula involves a y -value that is on the order of a thousand trillion trillion trillion trillion trillion trillion! One of the challenges (the tenth one) that David Hilbert threw down to twentieth-century mathematicians in his famous list was to find a general method for solving equations of this type. In 1970, however, the Russian mathematician Yuri Matiyasevich showed that there is no general algorithm for determining whether a particular Diophantine equation is soluble: the problem is undecidable.

3. Diophantine Equation - English Dictionary english to english dictionary containing references. http://www.online-dictionary.biz/english/vocabulary/reference/diophantine_equati

var language=0; var from='english'; var to='english'; Online Dictionary Chinese to English English to Chinese ... French to English German to English to Japanese Italian to English Japanese to English to German Latin to English Russian to English ... Swedish to English If you can't find the translation you need, try our free translation Diophantine Equation - English Dictionary 1. Diophantine equation Equations with integer coefficients to which integer solutions are sought. Because the results are restricted to integers, different algorithms must be used from those which find real solutions. [More details?] A B C D ... Z All content on this website is property of LocalTranslation unless stated otherwise. document.getElementById("generationTime").innerHTML='('+(0.52)+' seconds)'; document.getElementById("generationTime").innerHTML='('+(0.52)+' seconds)';

4. Diophantine Equation - Wikipedia Diophantine equation. Diophantine equations are equations of the form f = 0, where f is a polynomial with integer coefficients in one or several variables http://facetroughgemstones.com/wikipedia/di/Diophantine_equation.html

Office Supplies Buy Posters A-Z Products Website Advertising ... Diophantine equation Diophantine equations are equations of the form f = 0, where f is a polynomial with integer coefficients in one or several variables which take on integral values. They are named after Diophantus who studied equations with variables which take on rational values. Examples of Diophantine equations are ax by = 1: See Bézout's identity x n y n z n : For n =2 there are 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. x n y Pell's equation ) which is named, mistakenly, after the English mathematician John Pell[?] . It was studied by Fermat The depth of the study of general Diophantine equations is shown by the characterisation of Diophantine sets as recursively enumerable The field of Diophantine approximation deals with the cases of Diophantine inequalities : variables are still supposed to be integral, but some coefficients may be irrational numbers, and the equality sign is replaced by upper and lower bounds. wikipedia.org

5. Diophantine Equation - AoPSWiki Retrieved from http//www.mathlinks.ro/Wiki/index.php/diophantine_equation . Category Number Theory. Views. Article; Discussion; Edit; History; Move http://www.mathlinks.ro/Wiki/index.php/Diophantine_equation

Home Art of Problem Solving WOOT! Books ... Log in Diophantine equation From AoPSWiki A Diophantine equation is an equation relating integer (or sometimes natural number or whole number ) quanitites. Finding the solution or solutions to a Diophantine equation is closely tied to modular arithmetic and number theory . Often, when a Diophantine equation has infinitely many solutions, parametric form is used to express the relation between the variables of the equation. Diophantine equations are named for the ancient Greek/Alexandrian mathematician Diophantus. Contents Linear Combination Pythagorean Triples Method of Pythagoras Method of Plato ... See also Linear Combination A Diophantine equation in the form is known as a linear combination. If two relatively prime integers and are written in this form with , the equation will have an infinite number of solutions. More generally, there will always be an infinite number of solutions when . If , then there are no solutions to the equation. To see why, consider the equation is a divisor of the LHS (also notice that must always be an integer). However

6. Algebraic.net - Math_Discover: Diophantine Equation http//granite.sru.edu/~venkatra/diophantine_equation.htm. Mathematical Applets http//www.wikipedia.org/wiki/diophantine_equation. The Beal Conjecture http://www.algebraic.net/math_discover/diophantine_equation.html

Algebraic.net Home - Diophantine Equation Books Popular Music Classical Music DVD VHS Toys Baby Computers Video Games Electronics Software Office Products Magazines Outdoor Living Kitchen Travel Images Newsgroups 1-20 of 79 Next 20 Diophantine Equation: Geometric Theorems, Diophantine Equations, and Arithmetic Functions by Jozsef Sandor , June, 2002 Diophantus and Diophantine Equations by Isabella G. Bashmakova , November, 1997 The Algorithmic Resolution of Diophantine Equations : A Computational Cookbook by Nigel P. Smart , January, 1999 Diophantine Equations over Function Fields by R. C. Mason , July, 1984 Exponential Diophantine Equations by T. N. Shorey R. Tijdeman , March, 1987 Equations in Free Semigroups by Steklov Inst Math Academy Sci U.S.S.R. Staff , June, 1976 Diophantine Equations and Power Integral Bases: New Computational Methods by Istvan Gaal , May, 2002 Arithmetic of Algebraic Curves (Monographs in Contemporary Mathematics) by Serguel A. Stepanov Irene Aleksanova , December, 1994 Diophantine Approximations and Diophantine Equations (Lecture Notes in Mathematics, Vol. 1467) by Wolfgang M. Schmidt

7. Diophantine Equation - Wiktionary Retrieved from http//en.wiktionary.org/wiki/diophantine_equation . Categories English nouns Number theory Mathematics Algebra http://en.wiktionary.org/wiki/Diophantine_equation

Diophantine equation From Wiktionary Jump to: navigation search edit English edit Noun Singular Diophantine equation Plural Diophantine equations Diophantine equation plural Diophantine equations Wikipedia has an article on: Diophantine equation Wikipedia number theory A polynomial equation whose variables are only permitted to assume integer values Retrieved from " http://en.wiktionary.org/wiki/Diophantine_equation Categories English nouns Number theory ... Algebra Views Entry Discussion Edit History Personal tools Log in / create account Navigation Main Page Community portal Requested entries Recent changes ... Contact us Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 02:41, 2 February 2007. Content is available under GNU Free Documentation License About Wiktionary

8. 2006-05-18 Wikipedia/32P 47;Comas_Solá 8.801 A 6.692 AU 2014 1944 diophantine_equation. name. 1657. time. France. name. Pierre_de_Fermat diophantine_equation. name. Quadratic_equation. name. Chakravala_method http://www.alvis.info/alvis_docs/wp_18052006/320.xml.gz

9. Pell's Equation http//www.4reference.net/encyclopedias/wikipedia/diophantine_equation.html . http//opensite.org/Science/Mathematics/Number_Theory/diophantine_equation http://www.scienceoxygen.com/math/317.html

Science Oxygen Home Science Projects Study Reference Notes ... Origins of some arithmetic terms #2... http://www.pballew.net/arithme2.html Varga Prakriti... http://www.math.sfu.ca/histmath/India/7thCenturyAD/Varga_Prakriti.html Method of Hidden Parameters and Pell's Equation... http://adsabs.harvard.edu/abs/2003math......3176A Pell's equation references... http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Printref/Pell.html Dissertationsdatenbank... http://www.arcs.ac.at/dissdb/rn038296 UniMelb UGHB96 : 618-312 Number Theory... http://www.unimelb.edu.au/HB/1996/Sci/618/618-312.html Proceedings of the American Mathematical Society... http://www.ams.org/proc/2003-131-04/S0002-9939-02-06934-4/home.html AoPS Math Forum :: View topic - 2^x 3^y - 5^z 7^w = 1... http://www.artofproblemsolving.com/Forum/topic-24692.html Reducing to Pell's equation. - Information Technology Services... http://www.physicsforums.com/archive/topic/t-24214_Reducing_to_Pell's_equat Barbeau, E.J.... http://www4.ocn.ne.jp/~mmryhk/fbook/b/b07.html Access Denied...

10. CodeGuru Forums - [RESOLVED] Mathematical Formula FWIW, I think these types of problems are called Diophantine equations http//en.wikipedia.org/wiki/diophantine_equation Similar, but not the same. http://www.codeguru.com/forum/archive/index.php/t-441218.html

CodeGuru Forums General Discussion General Developer Topics PDA Click to See Complete Forum and Search > [RESOLVED] Mathematical Formula HanneSThEGreaT December 12th, 2007, 07:17 AM Hello guys, seems like I'm making a habit of asking questions these days. :rolleyes: I'm busy making an automatic exam generator, whereby I input details about the exam, then the questions and so on. It is basically at a stage where I could already implement it, but there is a feature I'd like to include, and by doing that, will make the application more user friendly. Let me explain. If have used / seen Microsoft Excel's Solver utility, you'd know that I can tell Solver that I'm working with x amount ( say, 500000 ), and I need to buy at least 2 big cars, 3 medium cars, and 4 small cars with that 500000. Right, so now I can set Solver's constraints in order to achieve that. It show me that I can buy 10 small cars, 6 medium cars, and 6 big cars. If I were to change the original total to 490 000, it will show me that I can buy 5 small cars, 7 medium cars, and 7 big cars. So now, I think I'm looking for something similar to this. Basically, I need to be able to input 50 ( the theory section's total marks ), and be able to generate an automatic point scheme, with questions counting 2 marks, 3, 4, 5, and 1. I need to be able to give all available possibilities and have used all marks. Understand what I mean ¿

11. Talk:Diophantine Equation - AoPSWiki Retrieved from http//www.artofproblemsolving.com/Wiki/index. php/Talkdiophantine_equation . Categories Words of the Week Article of the Day http://www.artofproblemsolving.com/Wiki/index.php/Talk:Diophantine_equation

AoPSWiki Preparing for MATHCOUNTS or the AMC contests, and having a tough time with number theory problems? Read Art of Problem Solving's Introduction to Number Theory by Mathew Crawford. Page Discussion View source History Personal tools Log in / create account Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link Talk:Diophantine equation From AoPSWiki AoPSWiki Words of the Week for December 13-19 Previous week Fibonacci sequence Siemens Competition Current week William Lowell Putnam Mathematical Competition Diophantine equation Next week Graph (graph theory) Carl Friedrich Gauss AoPSWiki Article of the Day Diophantine equation was the AoPSWiki Article of the Day for December 17, 2007 Retrieved from " http://www.artofproblemsolving.com/Wiki/index.php/Talk:Diophantine_equation

12. Diophantine Equation Retrieved from http//en.wikipedia.org/wiki/diophantine_equation . Categories Diophantine equations. Source this wikipedia article, under GFDL. http://www.algebra.com/algebra/homework/equations/Diophantine_equation.wikipedia

Diophantine equation Algebra Algebra Equations -> Diophantine equation ( Log On Ad: : algebra software that solves YOUR algebra homework problems with step-by-step help! Algebra: Equations Solvers Lessons ... In Depth Diophantine equation Jump to: navigation search 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. In more technical language, they define an algebraic curve algebraic surface or more general object, and ask about the lattice points on it. The word Diophantine refers to the Hellenistic mathematician of the 3rd century, 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.

13. Diophantine Equation - Indopedia, The Indological Knowledgebase Retrieved from http//www.indopedia.org/diophantine_equation.html . This page has been accessed 1047 times. This page was last modified 0240, http://www.indopedia.org/Diophantine_equation.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch Categories Diophantine equations Printable version ... Wikipedia Article Diophantine equation ज्ञानकोश: - The Indological Knowledgebase In mathematics , a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. A Diophantine problem is given as a Diophantine equation, whose solutions are the possible assignments of integers for the unknowns for which the equation is satisfied. 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 showTocToggle("show","hide") 1 Examples of Diophantine equations 2 Diophantine analyisis 2.1 Traditional questions 2.2 Hilbert's tenth problem ... edit Examples of Diophantine equations ax by = 1: See Bézout's identity ; this is a linear Diophantine.

14. Diophantine Equation - ᏗᎪᏪᎵ ᎦᏧᎾᎳ Ꭶ� Diophantine Equation. PlanetMath. http//chr. wikigadugi.org/wiki/diophantine_equation . Diophantine equations http://chr.wikigadugi.org/wiki/Diophantine_equation

Diophantine equation Diophantine equation (ᎢᏗᎦᏘᎭ) indeterminate (ᎤᏝᏠᏓᏕᎲ) polynomial equation (ᎢᏗᎦᏘᎭ) Ꮎ ᎠᎵᏍᎪᎸᏙᏗ ᎯᎠ variables (ᏧᏓᎴᏀᎢ) ᎾᏍᏋ integer (ᏂᎦᏛ) ᎾᏍᎩ ᎤᏩᏒ. Diophantine ᏗᎦᏎᏍᏙᏗ ᎤᎭ ᎦᏲᎳᎨᎢᏍᏗ equations (ᏗᏎᏍᏗ) ᎬᎾᏬᏍᎬ unknown (ᎤᎾᏠᏛ) variables (ᏧᏓᎴᏀᎢ) ᎠᎴ ᎠᏓᏠᏯᏍᏙᏗ ᎥᏩᏘᏍᎬ integers (ᏂᎦᏛ) Ꮎ ᏗᎦᎸᏫᏍᏓᏁᏗ ᎪᏢᎯᏌᏠᎯ ᎢᏳᏓᎵᎭ equations (ᏗᏎᏍᏗ). ᎭᏫᎾᏗᏢ ᎤᏟ ᎢᎦᎢ ᎤᏦᏍᏗ ᏂᎬᎿᏠᎦᏬᏂᎯᏍᏗ, ᎤᏠᏌ ᎧᏁᎢᏍᏔᏠᎯ algebraic (ᏗᏎᏍᏗ) ᎠᏓᏲᎲ algebraic (ᏗᏎᏍᏗ) ᎦᏚᎢ lattice (ᏗᎦᎾᏗᏫᏍᏗ) ᎪᏍᏓᏱ Diophantine Hellenistic mathematician (ᏗᏎᏍᏗ) ᎯᎠ 3rd ᏍᎪᎯᏧᏈ ᏧᏕᏘᏴᏗ, Diophantus , ᎦᎪ ᎪᏢᏠᎯ ᎠᎦᏎᏍᏙᏗ ᏯᏛᎿ equations (ᏗᏎᏍᏗ) ᎠᎴ ᏥᏄᏍᏛᎩ ᏌᏊ ᎪᎷᏩᏛᏗ mathematicians (ᏗᏎᏍᏗ) ᎬᏂᎨᏒ ᎢᏯᏓᏛᏁᏗ symbolism (ᏗᎬᏟᎶᏍᏙᏗ) . ᎯᎠ mathematical (ᏚᏳᎪᏛ) ᎠᎦᏎᏍᏙᏗ Diophantine ᏗᎦᏎᏍᏙᏗ Diophantus initiated (ᎠᏓᏕᎳᏗᏍᏗ) ᎨᏒᎢ ᎾᏊ ᎤᏯᏠᎲ "Diophantine ᏗᎫᎪᏙᏗ ᎢᎬᏁᏗ". linear (ᎠᏍᏆᏗᏍᏗ) Diophantine equation (ᎢᏗᎦᏘᎭ) ᎨᏒᎢ equation (ᎢᏗᎦᏘᎭ) ᎠᏰᎵ ᏔᎵ sums (ᎢᎦᎢ) monomials ᏀᎢᏳᎢ ᎠᏂᏏᏴᏫᎭ equations (ᏗᏎᏍᏗ) ᎡᏙᎠ ᎤᏓᏠᏗ ᎤᏦᏍᏗ ᎠᎴ ᏄᎵᏍᏔᏠᎠᎦᏎᏍᏔᏠᏂᎦᏠᎯᏒ ᎧᏃᎮᏍᎩ, ᎯᎠ formulation (ᎠᏃᏪᎵᏍᎬ) ᏂᎦᎥ theories (ᎪᎷᏩᏛᏗ) Diophantine equations (ᏗᏎᏍᏗ) (ᎤᏗᏗᏢ ᎢᎪᎯᏓ ᎪᎷᏩᏛᏗ

15. Keyword: Diophantine Equation The Petri Nets Bibliography Keyword diophantine equation. http://www.informatik.uni-hamburg.de/TGI/pnbib/keywords/d/diophantine_equation.h

For the most recent entries see the Petri Nets Newsletter Keyword: diophantine equation Zaitsev, D.A. Theoretical grounding of Toudic's method. Zaitsev, Dmitry A. Formal Grounding of Toudic Method. Do you need a refined search? Try our search engine which allows complex field-based queries. Back to the Petri Nets Bibliography

16. Diophantine Equation - MathEclipse symbolic math, eclipse, wiki, ajax, calculator, plotter, computer algebra, java, mathematic. http://www.matheclipse.org/en/Diophantine_equation

Home Online Symbolic Calculator Recent Changes Search ... Upload File Wikipedia API Project Java Wikipedia API (bliki engine) Bliki Javadoc Eclipse Wikipedia Editor Nested Lists API Nested Lists API Nested Lists API Javadoc MathEclipse.org Project Eclipse Plugin MathEclipse Parser API MathEclipse Forum SourceForge Project Page ... Used Open Source Tools Java TM Applets integrated in the wiki pages, require a recent Java Plug-in installed on your computer and activated in your web browser. Login Register Article Comments ... Print Diophantine equation The topic "Diophantine equation" does not currently exist. To create it please follow the link: Diophantine equation JAMWiki Version 0.6.0

17. Diophantine Equation | English | Dictionary & Translation By Babylon Diophantine equation. Dictionary terms for Diophantine equation in English, English definition for Diophantine equation, Thesaurus and Translations of http://www.babylon.com/definition/Diophantine_equation/English

Diophantine equation Define Diophantine equation Translate Diophantine equation Wikipedia English The Free Encyclopedia Download this dictionary 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. In more technical language, they define an algebraic curve algebraic surface or more general object, and ask about the lattice points on it. See more at Wikipedia.org... This article uses material from Wikipedia and is licensed under the GNU Free Documentation License FOLDOC Dictionary Download this dictionary Diophantine equation mathematics integer coefficients to which integer solutions are sought. Because the results are restricted to integers, different algorithms must be used from those which find real solutions. [More details?] Translate: English Chinese (S) Chinese (T) Croatian Dutch French German Hebrew Italian Japanese Korean Portuguese Russian Serbian Spanish Swedish Turkish Additional Use Babylon to translate to various languages

18. Wiki Diophantine Equation Wiki Diophantine equation. Contents 1. Examples of Diophantine equations 2. Diophantine analysis 2. 1. Typical questions http://wapedia.mobi/en/Diophantine_equation

Wiki: Diophantine equation Contents: 1. Examples of Diophantine equations 2. Diophantine analysis 2. 1. Typical questions 2. 2. Diophantine analysis in India ... Wapedia: For Wikipedia on mobile phones

19. DIOPHANTINE EQUATION Computing. Diophantine equation Equations with integer coefficients to which integer solutions are sought. Because the results are restricted to integers, http://www.websters-online-dictionary.org/Di/Diophantine_equation.html

20. Diophantine Equation Definition - Dictionary - MSN Encarta MSN homeMailMy MSNSign in. encartagreeting cardsmore. Envelope Hotmail im Messenger Figure of person in front of computer monitor My MSN http://encarta.msn.com/dictionary_1861604809/diophantine_equation.html

var s_account="msnportalencarta"; MSN home Mail My MSN Sign in ... more Hotmail Messenger My MSN MSN Directory Air Tickets/Travel Autos City Guides Election 2008 ... More Additional Reference Materials Thesaurus Translations Multimedia Other Resources Education Resources Math Help Foreign Language Help Project Planner ... Help Dictionary Find in Dictionary Thesaurus Translations A B ... See pronunciation key Search for " Diophant... equation " in all of MSN Encarta E-mail this entry Blog about this entry on MSN Spaces Download the MSN Encarta Right-Click Dictionary Diophantine equation Di·o·phan·tine e·qua·tion plural Di·o·phan·tine e·qua·tions noun Definition: algebraic equation: an algebraic equation that contains two or more variables, has only whole-number integral coefficients, and has integral solutions for the variables After Diophantus (fl. 3th century bc ), Greek mathematician Advertisement Also on Encarta 10 tips for building your English vocabulary 7 tips for funding an online degree How to succeed in the fashion industry without being a top designer Alternatives to the M.B.A. ... Coffee break: Recharge your brain Our Partners ApplyWise Online College Admissions Counseling ClassesUSA.com: Compare online degrees

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