1. Diophantine Equation - Wikipedia, The Free Encyclopedia In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. 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 (beyond the theory of quadratic forms ) was an achievement of the twentieth century.

2. Diophantine Equation Matiyasevich showed that there is no general algorithm for determining whether a particular Diophantine equation is soluble the problem is undecidable . 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!

3. Diophantine Equation - AoPSWiki Jun 11, 2009 A Diophantine equation is an equation relating integer (or sometimes natural number or whole number) quanitites. http://www.artofproblemsolving.com/Wiki/index.php/Diophantine_equation

Art of Problem Solving LOGIN/REGISTER Home Bookstore AoPS Curriculum ... Articles You are here: Resources AoPSWiki Search Wiki Page Tools Page Discussion View source History Personal tools Talk for this IP Log in Navigation Main Page Community portal Current events Recent changes ... Help Toolbox What links here Related changes Special pages Printable version ... Permanent link 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

4. Diophantine Equation - Definition In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. http://www.wordiq.com/definition/Diophantine_equation

Diophantine equation - Definition 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 analysis 2.1 Traditional questions 2.2 Hilbert's tenth problem ... 3 External links Examples of Diophantine equations ax by = 1: See Bézout's identity ; this is a linear Diophantine. x n y n z n : For n = 2 there are many solutions ( x y z ), the

5. Diophantine Equation - Wiktionary Aug 5, 2010 Wikipedia Diophantine equation (plural Diophantine equations) Retrieved from http//en.wiktionary.org/wiki/diophantine_equation http://en.wiktionary.org/wiki/Diophantine_equation

Diophantine equation Definition from Wiktionary, the free dictionary Jump to: navigation search edit English edit Noun Wikipedia has an article on: Diophantine equation Wikipedia Diophantine equation plural Diophantine equations number theory A polynomial equation whose variables are only permitted to assume integer values edit Translations polynomial equation French: équation diophantienne fr (fr) f Hungarian: diophantoszi egyenlet hu (hu) Italian: equazione diofantea it (it) equazione diofantina ... (it) Swedish: diofantisk ekvation sv (sv) c Retrieved from " http://en.wiktionary.org/wiki/Diophantine_equation Categories English nouns Number theory ... Algebra Personal tools New features Log in / create account Namespaces Entry Discussion Variants Views Read Edit History Actions Search Navigation Main Page Community portal Preferences Requested entries ... Contact us Toolbox What links here Related changes Upload file Special pages ... Permanent link In other languages Svenska This page was last modified on 5 August 2010, at 16:29. Text is available under the Creative Commons Attribution/Share-Alike License ; additional terms may apply. See for details.

6. Diophantine Equation | TripAtlas.com In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than http://tripatlas.com/Diophantine_analysis

7. Diophantine Equation - Wikipedia@pedia Diophantine equationIn mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer http://wikipedia.atpedia.com/en/articles/d/i/o/Diophantine_equation.html

wikipedia＠pedia wikipedia@PEDIA is study site of the language based on Wikipedia. TOP Translation Select text and it is translated. to AFRIKAANS to ALBANIAN to AMHARIC to ARABIC to ARMENIAN to AZERBAIJANI to BASQUE to BELARUSIAN to BENGALI to BIHARI to BULGARIAN to BURMESE to CATALAN to CHEROKEE to CHINESE to CROATIAN to CZECH to DANISH to DHIVEHI to DUTCH to ENGLISH to ESPERANTO to ESTONIAN to FILIPINO to FINNISH to FRENCH to GALICIAN to GEORGIAN to GERMAN to GREEK to GUARANI to GUJARATI to HEBREW to HINDI to HUNGARIAN to ICELANDIC to INDONESIAN to INUKTITUT to ITALIAN to JAPANESE to KANNADA to KAZAKH to KHMER to KOREAN to KURDISH to KYRGYZ to LAOTHIAN to LATVIAN to LITHUANIAN to MACEDONIAN to MALAY to MALAYALAM to MALTESE to MARATHI to MONGOLIAN to NEPALI to NORWEGIAN to ORIYA to PASHTO to PERSIAN to POLISH to PORTUGUESE to PUNJABI to ROMANIAN to RUSSIAN to SANSKRIT to SERBIAN to SINDHI to SINHALESE to SLOVAK to SLOVENIAN to SPANISH to SWAHILI to SWEDISH to TAJIK to TAMIL to TAGALOG to TELUGU to THAI to TIBETAN to TURKISH to UKRAINIAN to URDU to UZBEK to UIGHUR to VIETNAMESE This area is result which is translated word.

8. Diophantine Equation www.algebra.com/algebra/ /diophantine_equation.wikipediaDiophantine equationDiophantine equation. Diophantine equations are equations of the form f = 0, where f is a polynomial with integer coefficients in one or several variables http://www.algebra.com/algebra/homework/equations/Diophantine_equation.wikipedia

9. Diophantine Equation In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. http://www.india-karnataka.info/Diophantine_equation

10. Diophantine Equation : Exponential Diophantine Equations Diophantine equation Exponential Diophantine Equations images, discuss, define , news. http://www.servinghistory.com/topics/Diophantine_equation::sub::Exponential_Diop

11. Diophantine_equation | Define Diophantine_equation At Dictionary.com –noun Mathematics . an equation involving more than one variable in which the coefficients of the variables are integers and for which integral solutions are sought. Use http://dictionary.reference.com/browse/Diophantine_equation

12. Math Lessons - Diophantine Equation 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 http://www.mathdaily.com/lessons/Diophantine_equation

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Diophantine equations Diophantine equation 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 analysis 2.1 Traditional questions

13. Diophantine Equation - California State University, Long Beach File Format Microsoft Excel View as HTML http://www.csulb.edu/~rmena/Number_Theory/diophantine_equation.xls

D_Nw HXu͉Q$���@�qڃ)=��hOȿ����E�?"����iz�)m��Y~���Ҕ��$m>-߈mݷh �m�� 6��Tw��[�kFX ��10m��V$���m(#��Xn �÷����+��0L[s�4#�������€o �ww?dj��MGނz�"�R�i���:���� A H$d ���� 4D� ���É c���ׯ����(ͣ=G��6?�MMT.������-55@)JP R����)@Wud �h~,E�j��~3n%p�i�IŠN �*�O+Q�.���H� �j�4�� ���x � Nj���J*_�:�'��Q�!_��ʌ��F�Ҟ@�t�*kw <��j����V�"L-�#�X��(ߐ3RT��ug�ѽ�j�m�^�U�~�$)�=v�-% J�WPc ' <�Z qh�q��������w� <�+��#Sp�_`]��˲��f <�蔠��(Sj5�'��-���wYjRT�[%J� � <�,Q�����;Hm+8ܾ�)ϰx� /Ōs��d�j����mb�nV�1�^+qm��#h n� �Gjа��7mPͧQCi�����y�������pFJT2��^�%�:��h��aAz%��[i�A�ڂ���� �>�3Y�_�9��˞�Ҽ��y5E��= ��k�`ޙ�,�Q�)6��(U�#β���P�3W܆��Km%k.����(��� < �v��梈���Z�k+]�L0�����ʔ%�z�)A=�O) <�B��b����vx� ������#�"qD��fW�w���İ�-��[�*���- ����d� <�3�+�Ԗ�n�pi�$1-;��h� <��)gh`�O�$�� '�d�� �J�gU�bcʛ�� B��SKam$� C�+��¾��k������.S=f iiK��DT Nr <ۣ�0�U�s�ʖ��@� <��~��қ�kN��.�q`@� *-l��!���毎ˌ�̲�u�R���$$��Y�*(��p�~��g���o��jm�6��3�X#�� �ꕨ�˝r� Ɓ5�H���*�GZ7�%*)�c�,��)�h�����v���8��-d��kd� ��"�N/s^�̄��i撡�_iM���@���t�=u �Š�7�r��*�o����� K�yOt� ջXb"Cq[D�Zu� <��Qh��Hq[� ��d��$�����z�d]�ti�-�ɖ����7%ek%JJ�t�e <c�y��.���k�um����[+J �;�9��x

14. Diophantine Equation | Ask.com Encyclopedia In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than http://www.ask.com/wiki/Diophantine_equation?qsrc=3044

15. Glossary: Diophantine Equation diophantine equation. A Diophantine equation is one which is to be solved for integer solutions only. http://www-history.mcs.st-and.ac.uk/Glossary/diophantine_equation.html

diophantine equation A Diophantine equation is one which is to be solved for integer solutions only.

16. Category:Diophantine Equation - Wikimedia Commons Nov 6, 2008 CategoryDiophantine equation. From Wikimedia Commons, the free media repository . Jump to navigation, search http://commons.wikimedia.org/wiki/Category:Diophantine_equation

Category:Diophantine equation From Wikimedia Commons, the free media repository Jump to: navigation search Subcategories This category has only the following subcategory. L Linear diophantine equation (5 F) Retrieved from " http://commons.wikimedia.org/wiki/Category:Diophantine_equation Category Number theory Personal tools New features Log in / create account Namespaces Category Discussion Variants Views View Edit View history Actions Search Navigation Main Page Welcome Community portal Village pump Participate Upload file Recent changes Latest files Random file ... Donate Toolbox What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 6 November 2008, at 08:45. Text is available under the Creative Commons Attribution/Share-Alike License ; additional terms may apply. See for details. About Wikimedia Commons

17. Pirates Dividing Loot Question- NEW See http//en.wikipedia.org/wiki/diophantine_equation for an explanation. You have. A = 1024B/27 14/27 = 37B + (25B - 14)/27. Since A and B are integers, http://www.physicsforums.com/showthread.php?t=265284

18. Diophantine Equation - On Opentopia, Find Out More About Diophantine Equation In mathematics, a Diophantine equation is an indeterminate polynomial equation that only allows the variables to be integer s. Diophantine problems have fewer equations than http://encycl.opentopia.com/term/Diophantine_equation

About Opentopia Opentopia Directory Encyclopedia ... Tools Diophantine equation Encyclopedia D DI DIO : Diophantine equation In mathematics , a Diophantine equation is an indeterminate polynomial equation that only allows the variables to be integer s. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. The word Diophantine refers to the Hellenistic mathematician of the 3rd century CE Diophantus of Alexandria Egypt 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 1 Examples of Diophantine equations 2 Diophantine analysis 2.1 Traditional questions 2.2 Diophantine analysis in India ... 4 External links Examples of Diophantine equations ax by = 1: See Bézout'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

19. Diophantine Equation In Finnish - Dictionary And Translation Translate this page Diophantine equation. Dictionary terms for Diophantine equation in Finnish, Finnish definition for Diophantine equation, Thesaurus and Translations of http://www.babylon.com/definition/Diophantine_equation/Finnish

20. Diophantine Equation Summary | BookRags.com Diophantine equation. Diophantine equation summary with 5 pages of encyclopedia entries, research information, and more. http://www.bookrags.com/wiki/Diophantine_equation

Page 1     1-20 of 145    1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | Next 20