101. Diophantine Equation Definition | Blog Bisnis Online Translate this page diophantine equation dictionary definition and pronunciation diophantine equation definition and more from the free merriam. Definition of word from the http://masroy.net/tag/diophantine equation definition

102. Diophantine Equation Definition Of Diophantine Equation In The Free Online Encyc (mathematics) Diophantine equation Equations with integer coefficients to which integer solutions are sought. Because the results are restricted to integers, different http://encyclopedia2.thefreedictionary.com/Diophantine equation

103. Taxicab Numbers David W. Wilson s list of the smallest number that can be expressed as a sum of two positive cubes in n different ways, for n = 1 through 5. http://pi.lacim.uqam.ca/eng/problem_en.html

Taxicab Numbers To many mathematicians, the mere mention of the number 1729 recalls the following incident involving mathematicians G.H. Hardy and Srinivasa Ramanujan: Once, in the taxi from London [to Putney], Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen. "No, Hardy," said Ramanujan. "It is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways." [1] In memory of this incident, the least number which is the sum of two positive cubes in n different ways is called the n th taxicab number, which I will denote Taxicab( n . In [2], it is shown that for any n n ways, which guarantees the existence of Taxicab( n for n Taxicab(1) = is so trivial as not to count as a discovery. Taxicab(2) = Taxicab(3) = was found by Leech in 1957. Taxicab(4) = was found by E. Rosenstiel, J.A. Dardis, and C.R. Rosenstiel in 1991 [3].

104. Diophantine Equation | Facebook Welcome to the Facebook Community Page about Diophantine equation, a collection of shared knowledge concerning Diophantine equation. http://www.facebook.com/pages/Diophantine-equation/109271249099125

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105. The Fifth Taxicab Number Is 48988659276962496 David W. Wilson s article on his search for the smallest integer that can be expressed as a sum of two positive cubes in 5 distinct ways, up to order of summands. http://www.cs.uwaterloo.ca/journals/JIS/wilson10.html

Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.9 The Fifth Taxicab Number is 48988659276962496 David W. Wilson 263 E. Ricker Road Loudon, NH 03301 Email address: wilson@ctron.com Abstract: The n th taxicab number is the least number which can be expressed as a sum of two positive cubes in n distinct ways, up to order of summands. A brief history of taxicab numbers is given, along with a description of the computer search used by the author to find the 5th taxicab number, 48988659276962496. Additional results from the search are summarized. 1. Introduction The n th taxicab number is the least integer which can be expressed as a sum of two positive cubes in (at least) n distinct ways, up to order of summands. In , there is a constructive proof that for any n n ways as a sum of two cubes (hereafter, we will call such numbers n-way sums ). This guarantees the existence of a least n -way sum (that is, the n th taxicab number) for n is of no help in finding the least n -way sum. The first taxicab number is trivially Ta(1) = 2 Ta(2) = 1729 This particular number was immortalized by the following well-known incident involving G. H. Hardy and Srinivasa Ramanujan:

106. Diophantine Equation Definition - Dictionary - MSN Encarta Di o phan tine e qua tion d ə f n tn i kw y'n, d ə f ntin i kw y'n (plural Di o phan tine e qua tions) noun Definition http://encarta.msn.com/encnet/features/dictionary/DictionaryResults.aspx?refid=1

107. On Equal Sums Of Like Powers And Related Problems Classification of problems related to equal sums of like powers. http://www.cs.man.ac.uk/~rizos/EqualSums/

These pages are no longer maintained. They refer to results collected around 1994-1995 using idle time on a network of SUN workstations. The most interesting results (ie, those that were going beyond what was then known) were presented much later as a poster at HPCNE'98 (Published by Springer in Lecture Notes in Computer Science, vol. 1401, Apr. 1998), which is available here . A report (ref.5 in the paper) containing all the results found during this exercise is given here (sorry it is a bit messy!). For the current status, the definitive place to check is Jean-Charles Meyrignac's site On Equal Sums of Like Powers and Related Problems These pages provide information on a class of problems related to the diophantine equation x k + x k + ... x m k = y k + y k + ... y n k where x i , y j integers, and k is greater than or equal to zero. The problem is that of finding non-trivial solutions (that is, solutions where there is no x i equal to any y j and vice versa ) of the above equation. Equations of this form have a long history. It can be seen that for m=1, n=2, Equation has no solutions for k > 2 according to Fermat's Last Theorem. In 1769, this was generalised by Euler who conjectured that, for m=1, there are no solutions with k less than n. The first counterexample was found in 1966.

108. Univ At Albany Mathematics Information Service A collection of links based on the former e-math gopher archive. http://math.albany.edu:8010/g/Math/topics/fermat/

Wiles, Ribet, Shimura-Taniyama-Weil and Fermat's Last Theorem Much of the material that seeded this archive was copied from the former gopher archive pertaining to "Fermat's Last Theorem" at e-math.ams.org This archive is no longer being updated since its topic has reached full maturity. The gopher links in this archive have been made inoperative. That technology did provide a very efficient way to serve mailbox archives online. Proof of the full modular curve conjecture Richard Taylor's web site contains a preprint of an article by C. Breuil, B. Conrad, F. Diamond, and Taylor, ``On the modularity of elliptic curves over Q ...'', to appear in J. Amer. Math. Soc. Instructional Conference on Fermat's Last Theorem, August 2000 For advanced graduate students in mathematics, August 6-18 University of Illinois at Urbana-Champaign. Nigel Boston and Chris Skinner, are the organizers. Karl Rubin's Washington Lecture, January 2000 AMS-MAA-SIAM joint meeting lecture on Ranks of Elliptic Curves. At the same location see also his May 1999 "SUMO" lecture on the areas of rational right triangles (yet another topic related to elliptic curves [YATREC]) and more. Modular Forms, Elliptic Curves, and Related Topics, January 2000

109. Fermat's Last Theorem Is Solved An attempted elementary proof of FLT using binomial expansions. http://www.coolissues.com/mathematics/fermat.htm

PROOF OF FERMAT'S LAST THEOREM James Constant math@coolissues.com Fermat's Last Theorem is solved using the binomial series Moved to http://www.coolissues.com/mathematics/Fermat/fermat.htm

110. Diophantine Equation: Meaning And Definitions — Infoplease.com diophantine equation Definition and Pronunciation Find definitions for http://dictionary.infoplease.com/diophantine-equation

Site Map FAQ in All Infoplease Almanacs Biographies Dictionary Encyclopedia Spelling Checker Daily Almanac for Oct 31, 2010 Skip Navigation Home Halloween ... games, quizzes Editor's Favorites Halloween Infoplease's Facebook page Follow Infoplease on Twitter Conversion Calculator ... DK Daily Teach Search: Infoplease Info search tips Search: Biographies Bio search tips Share Dictionary Find definitions for: Pronunciation: u [key] Math. an equation involving more than one variable in which the coefficients of the variables are integers and for which integral solutions are sought. Random House Unabridged Dictionary, dioon diopside Cite Print ... Add to Reddit Related Content Daily Word Quiz: ailurophobia Analogy of the Day: Spelling Bee: reticent Crossword: Crossword Puzzle Guide Frequently Misspelled Words Frequently Mispronounced Words Easily Confused Words Find definitions for: Click Here! Click Here! Calculator Spelling Checker Place Finder Distance Calculator ... Year by Year 24 X 7 Private Tutor 24 x 7 Tutor Availability Unlimited Online Tutoring 1-on-1 Tutoring Explore Free Algebra Help Slope Formula RSS About Infoplease Part of Family Education Network Contact Link to Us Advertise with Infoplease Privacy ... Online Gradebook Click Here!

111. NOVA Online | The Proof NOVA Online presents The Proof, including an interview with Andrew Wiles, an essay on Sophie Germain, and the Pythagorean theorem. http://www.pbs.org/wgbh/nova/proof/

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112. Las Expresiones Regulares Como Exploradores De Un Árbol De Soluciones Translate this page In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. http://www.davioth.com/pl/node33.html

Sig: Número de substituciones realizadas Sup: Casos de Estudio Ant: Análisis de cadenas con Err: Si hallas una errata ... Subsecciones Números Primos Ecuaciones Diofánticas: Una solución Ecuaciones Diofánticas: Todas las soluciones Ecuaciones Diofánticas: Resolutor general ... Véase también Las Expresiones Regulares como Exploradores de un Árbol de Soluciones Números Primos El siguiente programa evalúa si un número es primo o no: Siguen varias ejecuciones: pl@nereida:~/Lperltesting$ ./isprime.pl 35.32 Usage: ./isprime.pl integer pl@nereida:~/Lperltesting$ ./isprime.pl 47 47 is prime pl@nereida:~/Lperltesting$ ./isprime.pl 137 137 is prime pl@nereida:~/Lperltesting$ ./isprime.pl 147 147 is 49 x 3 pl@nereida:~/Lperltesting$ ./isprime.pl 137 137 is prime pl@nereida:~/Lperltesting$ ./isprime.pl 49 49 is 7 x 7 pl@nereida:~/Lperltesting$ ./isprime.pl 47 47 is prime Ecuaciones Diofánticas: Una solución Según dice la entrada en la wikipedia: In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. La siguiente sesión con el depurador muestra como se puede resolver una ecuación lineal diofántica con coeficientes positivos usando una expresión regular: Ecuaciones Diofánticas: Todas las soluciones Usando el verbo (*FAIL) es posible obtener todas las soluciones: Ecuaciones Diofánticas: Resolutor general El siguiente programa recibe en línea de comandos los coeficientes y término inependeinte de una ecuación lineal diofántica con coeficientes positivos y muestra todas las soluciones. El algoritmo primero crea una cadena conteniendo el código Perl que contiene la expresión regular adecuada para pasar luego a evaluarlo:

113. Fermat's Last Theorem A historical and biographical account. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.htm

Fermat's last theorem Number Theory Index History Topics Index Version for printing Pierre de Fermat died in 1665. Today we think of Fermat as a number theorist, in fact as perhaps the most famous number theorist who ever lived. It is therefore surprising to find that Fermat was in fact a lawyer and only an amateur mathematician. Also surprising is the fact that he published only one mathematical paper in his life, and that was an anonymous article written as an appendix to a colleague's book. There is a statue of Fermat and his muse in his home town of Toulouse: (Click it to see a larger version) Because Fermat refused to publish his work, his friends feared that it would soon be forgotten unless something was done about it. His son, Samuel undertook the task of collecting Fermat 's letters and other mathematical papers, comments written in books, etc. with the object of publishing his father's mathematical ideas. In this way the famous 'Last theorem' came to be published. It was found by Samuel written as a marginal note in his father's copy of Diophantus 's Arithmetica Fermat's Last Theorem states that x n y n z n has no non-zero integer solutions for x y and z when n Fermat wrote I have discovered a truly remarkable proof which this margin is too small to contain.

114. Diophantine Equation Diophantine Equation Linear Abstract Algebra discussion So the other day I was asked a question about a problem by a friend. Having not been active in a math class in a http://www.physicsforums.com/showthread.php?t=260904

115. Fermat's Last Theorem -- From Wolfram MathWorld Article in Eric Weisstein s World of Mathematics. http://mathworld.wolfram.com/FermatsLastTheorem.html

116. Beal's Conjecture: A Search For Counterexamples Results of a computer search by Peter Norvig. http://www.norvig.com/beal.html

Beal's Conjecture: A Search for Counterexamples Beal's Conjecture is this: There are no positive integers x,m,y,n,z,r satisfying the equation x m + y n = z r where m,n,r x,y,z are co-prime (that is, gcd(x,y) = gcd(y,z) = gcd(x,z) There is a prize for the first proof or disproof of the conjecture. The conjecture is obviously related to Fermat's Last Theorem, which was proved true by Andrew Wiles in 1994. A wide array of sophisticated mathematical techniques could be used in the attempt to prove the conjecture true (and the majority of mathematicians competent to judge seem to believe that it likely is true). Less sophisticated mathematics and computer programming can be used to try to prove the conjecture false by finding a counterexample. This page documents my progress in this direction. There are two things that make this non-trivial. First, we quickly get beyond the range of 32 or 64 bit integers, so any program will need a way of dealing with arbitrary precision integers. Second, we need to search a very large space: there are six variables, and the only constraint on them is that the sum must add up. Suppose we wanted to search, all bases (

117. L�mites Computacionales Translate this page File Format PDF/Adobe Acrobat - Quick View http://people.cs.uchicago.edu/~borja/lectures/limites_computacionales.pdf

118. Diophantine Equation@Everything2.com An equation with any number of variables involving the basic arithmetic operations (addition, multiplication, and exponentiation) considering only integer solutions. http://www.everything2.com/title/Diophantine equation

Near Matches Ignore Exact Everything Diophantine equation thing by blaaf Tue Oct 10 2000 at 3:51:17 An equation with any number of variables involving the basic arithmetic operations ( addition multiplication , and exponentiation ) considering only integer solutions. It has been proven that the problem of solving general Diophantine equations is undecidable . Some have no solutions, others have a finite number of solutions, some have an infinite number of solutions. Particular cases can be solved by one means or another, and Diophantine analysis is a major branch of mathematics and number theory . However, for many Diophantine equations, it is impossible to determine whether or not solutions even exist. Example: y = x Solutions (probably incomplete): x y -9 19 -9 -19 -1 33 -1 -33 28,187,351 149,651,610,621 28,187,351 -149,651,610,621 I like it! C! printable version chaos ... Omega Y'know, if you log in , you can write something here, or contact authors directly on the site.

119. Karl Rubin Slides for a talk by Karl Rubin on the story of Fermat s Last Theorem for a general audience, including the history of the problem, the story of Andrew Wiles solution and the excitement surrounding it, and some of the many ideas used in his proof. http://math.stanford.edu/~rubin/lectures/fermatslides/

120. Beal's Conjecture Disproved for the same reasons Fermat s Last Theorem is proved by a binomial infinite series expansion http://www.coolissues.com/mathematics/Beal/beal.htm

BEAL'S CONJECTURE DISPROVED James Constant math@coolissues.com Beal's Conjecture is disproved for the same reasons Fermat's Last Theorem is proved. For simple proofs see http://www.coolissues.com/BealFermatPythagorasTriplets.htm http://www.coolissues.com/BealFermatPythagoras/proofs.htm http://www.coolissues.com/mathematics/Exponential/series.htm Beal's conjecture A prize is offered for proof or disproof of Beal's conjecture , stated as follows: If x,y,z,m,a,b positive integers then x,y,z have a common factor Proof of Fermat's Last Theorem A proof of Fermat's Last Theorem (FLT) is available using the binomial expansion . In this proof it is shown that z cannot be an integer in the equality x,y,z,m positive integers thus proving FLT x,y,z,m positive integers Disproof of Beal's Conjecture When a=b=m , Beal's equation (1) becomes Fermat's equation (2). Clearly, Fermat's equation (2) is a special case of Beal's equation (1). The same procedure used in Fermat's equation (2) can be used to show that z cannot be an integer in Beal's equation (1). Start by rearranging Beal's equation (1)

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