121. Solution - New Mexico Supercomputing Challenge Mini-Challenge File Format PDF/Adobe Acrobat Quick View http://www.challenge.nm.org/archive/09-10/ProjectEuler.net_139_Solution Explanat

122. Sci.math: Diophantine Equation This is an exercise in a textbook Use Gaussian integers to solve the Diophantine equation http://sci.tech-archive.net/Archive/sci.math/2004-12/9837.html

Diophantine equation From: Bart Goddard ( Date: Next message: valued customer: "elementary logic question of an apparent paradox" Previous message: Arndt Jonasson: "Re: Is zero even or odd?" Next in thread: Timothy Murphy: "Re: Diophantine equation" Reply: Timothy Murphy: "Re: Diophantine equation" Reply: Robert Israel: "Re: Diophantine equation" Reply: sttscitrans_at_tesco.net: "Re: Diophantine equation" Messages sorted by: [ date ] [ thread ] Date: 22 Dec 2004 16:10:04 GMT This is an exercise in a textbook: Use Gaussian integers to solve the Diophantine equation x^2+y^2=z^3. Hmmmm....I haven't seen this one before, and I'm a bit puzzled. It seems like there are lots of solutions, since if z is representable as the sum of two squares then so is z^3 and we should be able to find a parameterization along those lines. I haven't been able to get anywhere with it, so I'm wondering what y'all might say. Another, unrelated, question is that I need to express a prime p = 1 (mod 3) in the form u^2+3v^2. Certainly -3 is a quadratic residue mod p, which gives me

123. Stupid High School Math Problem. : Math Aug 30, 2010 This is what s called a Diophantine equation. You can find information on solving Diophantine equations in most elementary number theory http://en.reddit.com/r/math/comments/d7eo9/stupid_high_school_math_problem/

124. Fermat's Last Theorem Is Solved An attempted elementary proof of Fermat s Last Theorem by James Constant, rejecting that of Wiles. http://www.coolissues.com/mathematics/Fermat/fermat.htm

PROOF OF FERMAT'S LAST THEOREM James Constant math@coolissues.com Fermat's Last Theorem is solved using the binomial series A new theorem determining the irrationality of a number using its infinite series expansion is presented. 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 Introduction Fermat (1601-1665) claimed in 1637 to have discovered a marvelous proof of his last theorem. xyz x,y,z,m integers The Binomial Series Before seeking the solution to Fermat's last theorem, consider the binomial series in which a is an arbitrary number, positive or negative, rational or irrational. The Bounds of Exponent a The exact conditions under which the series, equation (2), is convergent are as follows 1. If index a is an integer the series terminates and is valid for all values of x and becomes the Binomial Theorem. 2. For all other values of a , the series is absolutely convergent for and divergent for 3. For

125. Papers On The 3x + 1 / 3n + 1 Problem, Fermat's Last Theorem, And Other Mathemat Provides papers on several mathematical subjects, including Fermat s Last Theorem and the 3x + 1 Problem. One paper offers reasons why we might be close to a solution of the latter problem. http://www.occampress.com

Welcome to Occam Press! Information about Occam Press and about this web site. A note to professional mathematicians. A note to graduate students. The following papers, essays, and notes by Peter Schorer: Papers on the 3 x + 1 Problem (aka the 3n + 1 Problem, the Syracuse Problem, etc.) including: "A Solution to the 3x + 1 Problem" ... Essay, "Notes Toward a Pragmatics-Based Linguistics" William Curtis's book, How to Improve Your Math Grades , which sets forth a radical new organization of mathematical subjects aimed at improving the speed of problem solving. Paper, "Good Mathematical Writing Style: Summary of Rules" Information about Occam Press: Occam Press is a small publisher located in Berkeley, CA. It was created to provide an outlet for independent scholars, including mathematicians and computer scientists working outside the university. We will be placing entire works on this web site. Interested persons will be able to buy printed copies directly from us. However, until the works have been placed on the web site, we offer brief descriptions of each. Interested persons may obtain sample pages, and more information, by e-mailing or calling us, or by sending us surface mail. Occam Press 2538 Milvia St.

126. Beal An elementary proof of Beal s Conjecture given the proof of Fermat s Last Theorem. http://beal.yolasite.com/

Home Beal ON THE FULL BEAL CONJECTURE The purpose here is to confirm Beal’s Conjecture, specifically as a consequence of Fermat’s Last Theorem (FLT) and a defining transform, T used to generalize the problem, all in context with conditions necessary to uniquely describe the values of all supposed solutions. Consider the sum of a and b which is now unspecified: a + b a and b can be “cross-defined,” (one in terms of the other) by the transform T: a to b m b to a n with m and n greater than 2 subject to the specification p q T a b b m + a n p q which is the general representation of Beal’s Conjecture when equivalence on the right is negated. T may reapplied such that it does nothing to change the conditions on a and b. Reapplying T: T a + b = T( b m + a n b mn a mn p q The latter is possible only when a = b = 2 (see: http://fermat.yolasite.com ), in which case, 2 mn mn mn+1 Now let m n p q and further, Then m-n m-n p q n again see: http://fermat.yolasite.com Otherwise, 2 r r r+1 which is factorable to 1 z z = 2 where a = b = 1 while p q is reduced to 2. In all other cases a , b and p are factorable such that the general representation fails to hold.

127. Artigos E T�picos P�gina 1 TEORIA DO ERRO TEORIA DOS JOGOS TEORIA Translate this page File Format PDF/Adobe Acrobat - Quick View http://www.inf.ufpr.br/cjp07/aprender.pdf

128. Finiteness Results For Diophantine Equations Involving Polynomial Families Thomas Stoll, TU Graz, 2003. Text (PS). http://www.dmg.tuwien.ac.at/stoll/thesis.html

129. Algorithmic Solution Of Diophantine Equations Thomas Stoll, TU Graz, 2001. Abstract, text (PS). http://www.dmg.tuwien.ac.at/stoll/diplthesis.html

130. Abderrahmane Nitaj Universit de Caen. Diophantine equations, the ABC conjecture, polynomials, elliptic curves, Szpiro s conjecture. http://www.math.unicaen.fr/~nitaj/

Abderrahmane Nitaj AfricaCrypt Conferences Web page AFRICACRYPT 2011 July 4-8, 2011 Dakar, Senegal Presentation The abc conjecture ... Contact The abc conjecture To the abc conjecture home page Back to top Research Interests Number Theory Diophantine Equations, the abc conjecture, Polynomials. Arithmetic Geometry Elliptic curves, Szpiro's conjecture. Cryptography Cryptosystems, The discrete logarithm problem, Elliptic curves. Implementation of Computer Algebra Algorithms SIMATH APECS PARI MAGMA ... LIDIA Fractals (Amateur) Fractal pictures, Animations. Back to top Thesis abc et de Szpiro. [DVI] [Postscript] Back to top Publications New vulnerabilities in RSA , Submitted to J Appl Math Comput. [PDF] A New Vulnerable Class of Exponents in RSA , Submitted to JP Journal of Algebra, Number Theory and Applications. [PDF] New weak RSA keys , Submitted to JP Journal of Algebra, Number Theory and Applications. [PDF] Cryptanalysis of RSA using the ratio of the primes , In Bart Preneel (Ed.): Progress in Cryptology - AFRICACRYPT 2009, Lecture Notes in Computer Science 5580 Springer 2009. Slides Application of ECM to a class of RSA keys , 12, No. 2, 121-137 (2009).

131. TRABAJO Una Simulaci�n Simplificada De La Criptograf�a Translate this page File Format PDF/Adobe Acrobat - Quick View http://www.uam.es/departamentos/ciencias/matematicas/premioUAM/premiados3/simula

132. Volker Ziegler TU Graz. Diophantine equations, especially Thue equations. Publications. http://finanz.math.tu-graz.ac.at/~ziegler/

Volker Ziegler Volker Ziegler Institute for Analysis and Computational Number Theory Graz University of Technology E-Mail: ziegler@math.tugraz.at Research: Thue equations Unit sum number problem Arithmetic progressions (and other sequences) on curves Discrepancy theory and metric number theory See also my publication list publication list. Teaching: In the winter semester 2010/11 I will supervise the following lectures: Mathematik C Mathematische Grundlagen der Kryptografie Computermathematik 1 Analysis T1 Private: I also do some sports: Climbing and Trampoline.

133. Home - Szabolcs Tengely University of Debrecen. Effective methods for Diophantine equations. Publications, thesis, software. http://www.math.klte.hu/~tengely/

Home Research List of Publications Number Theory ... Szabolcs Tengely Home Home Research Lectures Education ... Login Powered by LightNEasy 2.2.1 Original design: CSS Template by Rambling Soul

134. Index University of Crete. Explicit solution of diophantine equations. Publications. http://www.math.uoc.gr/~tzanakis/

Nikolaos G Tzanakis Professor of Mathematics Department of Mathematics University of Crete 714 09 IraklionCrete GREECE Office: E 309 Tel and fax: +30-2810-232962 (home), +30-2810-393839 (office) Home Address: 8 Solomou str., GR-713 06 IraklionCrete, GREECE E-mail: tzanakis@math.uoc.gr Research Area Explicit solution of diophantine equations Publications Teaching Now (Fall 2010) : Introduction to Algebra, Euclidean Geometry Web page of some courses (greek) Nikos G. Tzanakis Last update September 15, 2010

135. Wakabayashi, Isao Seikei University, Tokyo. Diophantine equations and transcendence problems for values of analytic functions. http://www.ge.seikei.ac.jp/wakaba/

136. Dr Francis Coghlan Homepage, Department Of Mathematics, Univ. Of Manchester, UK University of Manchester. Diophantine equations, elliptic curves. http://www.maths.manchester.ac.uk/DeptWeb/Homepages/fbc/

DEPARTMENT OF MATHEMATICS Dr Francis Coghlan Lecturer in Pure Mathematics Room 9.08 Department of Mathematics University of Manchester Oxford Road Manchester M13 9PL U.K. +44 (0)161 275 5856 (direct line) +44 (0)161 275 5819 (fax) +44 (0)161 275 5800 (general office) frank@ma.man.ac.uk Research Interests: Number Theory, Diophantine equations, elliptic curves. Publications Canadian Mathematical Bulletin. Vol.39(1) Back to the Departmental homepage Please send any feedback, comments or suggestions to the webmaster@maths.man.ac.uk Page last modified: January 14, 2002

137. Shorey, T. N. Tata Institute for Fundamental Research. Transcendence, Diophantine equations. Publications. http://www.math.tifr.res.in/~shorey/

138. Welcome To L�szl� Szalay's Home Page University of West Hungary. Diophantine equations. http://titanic.nyme.hu/~laszalay/

Dr. L�szl� Szalay associate professor Institute of Mathematics and Statistics Faculty of Economics University of West Hungary H-9400 Sopron, Erzs�bet u. 9. Tel: (36) 99 518-495 Fax: (36) 99 518-423 e-mail: laszalay@ktk.nyme.hu Last modified: 20. August 2010. Comments or notices on the page, please contact with

139. Fermat Corner Fermat s Last Theorem by Simon Singh. Discusses the early and recent history of people trying to solve this perplexing problem, including Andrew Wiles final success. Includes information about poems, limericks, the off-Broadway show and a quiz. http://www.simonsingh.net/Fermat_Corner.html

Fermat Corner Back to Homepage The Whole Story Who was Fermat? What is the Theorem? ... Wolfskehl Prize Andrew Wiles Fermat Corner Fermat�s Last Theorem is the most notorious problem in the history of mathematics and surrounding it is one of the greatest stories imaginable. This section explains what the theorem is, who invented it and who eventually proved it . When finished, it will also tell the fascinating stories of the some of the other mathematicians whose lives were tormented by this beautiful and intriguing problem. Fermat�s Last Theorem dominated my own life for four years, because I made a TV documentary, wrote a book and then lectured on the subject. Getting involved in Fermat�s mischievous conundrum set me on the path towards being an author and ignited an interest in mathematics that has continued ever since. As a physicist, I was always interested in mathematics as a tool for studying the universe, but learning about Fermat�s Last Theorem taught me to love mathematics for its own sake. There is a Mathematics Corner currently being developed for this site.

140. Cache:6FRYRufjibUJ:education.uncc.edu/cmste/summer/2005 Applications In Stat/Fer A brief biography of Fermat, details of his contributions to mathematics and information on his theory and the attempts to find a proof. http://209.85.229.132/search?q=cache:6FRYRufjibUJ:education.uncc.edu/cmste/summe

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