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Diophantine Equation: more books (88)

Advances in Algebra: An entry from Gale's <i>Science and Its Times</i> by Donald R. Franceschetti, 2001
The Birth of Number Theory: An entry from Gale's <i>Science and Its Times</i> by P. Andrew Karam, 2001
Quantitative Arithmetic of Projective Varieties (Progress in Mathematics) by Timothy D. Browning, 2009-10-23
Algorithmic Number Theory: 9th International Symposium, ANTS-IX, Nancy, France, July 19-23, 2010, Proceedings (Lecture Notes in Computer Science / Theoretical Computer Science and General Issues)
Equations in Free Semigroups (Proceedings of the Steklov Institute of Mathematics) by Steklov Inst Math Academy Sci U. S. S. R., 1976-06
Algebra in Ancient and Modern Times (Mathematical World) by V. S. Varadarajan, 1998-04-29
Ratner's Theorems on Unipotent Flows (Chicago Lectures in Mathematics) by Dave Witte Morris, 2005-08-15
Arithmetic of Algebraic Curves (Monographs in Contemporary Mathematics) by Serguei A. Stepanov, 1994-12-31
Comments and Topics on Smarandache Notions and Problems by Kenichiro Kashihara, 2008-10-10
Collected Papers (Vol. I), Scientific work by Florentin Smarandache, 2008-10-10
Number Theory: Volume II: Analytic andModern Tools (Graduate Texts in Mathematics) by Henri Cohen, 2007-05-23
One equation to rule them all (Rand Corporation. Research memorandum) by Martin Davis, 1968
Prime solutions of indeterminate equation wÂ²=xÂ²+yÂ²+zÂ² for all values of w=1 to 100 by Solomon Achillovich Joffe, 1914
The Pell equation by Edward Everett Whitford, 1912

lists with details

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
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
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

Extractions: 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) =
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
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

Extractions: 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. 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
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
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/

Extractions: 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.
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/

Extractions: 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
Fermat's Last Theorem Is Solved
An attempted elementary proof of FLT using binomial expansions.
http://www.coolissues.com/mathematics/fermat.htm
Diophantine Equation: Meaning And Definitions — Infoplease.com
diophantine equation Definition and Pronunciation Find definitions for
http://dictionary.infoplease.com/diophantine-equation

Extractions: games, quizzes Editor's Favorites Search: Infoplease Info search tips Search: Biographies Bio search tips Share 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 Related Content Find definitions for:
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/
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

Extractions: Subsecciones 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 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: Usando el verbo (*FAIL) es posible obtener todas las soluciones: 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:
Fermat's Last Theorem
A historical and biographical account.
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.htm

Extractions: 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. 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.
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
Fermat's Last Theorem -- From Wolfram MathWorld
Article in Eric Weisstein s World of Mathematics.
http://mathworld.wolfram.com/FermatsLastTheorem.html
Beal's Conjecture: A Search For Counterexamples
Results of a computer search by Peter Norvig.
http://www.norvig.com/beal.html

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

Extractions: Near Matches Ignore Exact 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):
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/
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

Extractions: 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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