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Diophantine Equation:     more books (88)

Theory of the linear diophantine equation, by Pedro Laborde, 1965 Existence and representation of diophantine and mixed diophantine solutions to linear equations and inequalities by A Charnes, 1975 Method of indeterminant coefficients in linear differential systems and the matrix equation XB - AX = U (MRC technical summary report) by Alberto Dou, 1964 On the multiple solutions of the Pell equation by D. H Lehmer, 1929 Number Theory: An Introduction to Mathematics (Universitext) by W.A. Coppel, 2009-08-12 Arithmetic of Quadratic Forms (Springer Monographs in Mathematics) by Goro Shimura, 2010-06-30 Analytic Number Theory: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11-18, 2002 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze) by J. B. Friedlander, D.R. Heath-Brown, et all 2006-10-19 Value Distribution Theory Related to Number Theory by Pei-Chu Hu, Chung-Chun Yang, 2006-07-26 Algorithmic Number Theory: 8th International Symposium, ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings (Lecture Notes in Computer Science / Theoretical Computer Science and General Issues) Logical Number Theory I: An Introduction (Universitext) (Vol 1) by Craig Smorynski, 1991-05-20 Topics from the Theory of Numbers (Modern Birkhäuser Classics) by Emil Grosswald, 2008-12-08 Catalan's Conjecture (Universitext) by René Schoof, 2008-11-13 Gerd Faltings: An entry from Gale's <i>Science and Its Times</i> by Adrienne Wilmoth Lerner, 2001 Arithmetic Geometry: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007 (Lecture Notes in Mathematics / Fondazione ... Firenze) (English and French Edition) by Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, et all 2010-11-29

lists with details

81. 1Up Science > Links Directory > Math: Number Theory: Diophantine Equations
    Math Number Theory diophantine equations . Uncover resources and links to Websites related to Math Number Theory diophantine equations .  
    http://www.1upscience.com/links/number-theory-diophantine-equations.html

82. Mathematical Publications By Benjamin M.M. De Weger
    Correction to the paper A hyperelliptic diophantine equation related to On elliptic diophantine equations that defy Thue s method the case of the  
    http://www.xs4all.nl/~deweger/publikaties.html

83. Randomness In Arithmetic
    The mathematical assertion that the diophantine equation with parameter k has no For any given pair of values of k and n, the diophantine equation has  
    http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer2.html
    
    Extractions: It is impossible to prove whether each member of a family of algebraic equations has a finite or an infinite number of solutions: the answers vary randomly and therefore elude mathematical reasoning. What could be more certain than the fact that 2 plus 2 equals 4? Since the time of the ancient Greeks mathematicians have believed there is little-if anything-as unequivocal as a proved theorem. In fact, mathematical statements that can be proved true have often been regarded as a more solid foundation for a system of thought than any maxim about morals or even physical objects. The 17th-century German mathematician and philosopher Gottfried Wilhelm Leibniz even envisioned a ``calculus'' of reasoning such that all disputes could one day be settled with the words ``Gentlemen, let us compute!'' By the beginning of this century symbolic logic had progressed to such an extent that the German mathematician David Hilbert declared that all mathematical questions are in principle decidable, and he confidently set out to codify once and for all the methods of mathematical reasoning. This result, which is part of a body of work called algorithmic information theory, is not a cause for pessimism; it does not portend anarchy or lawlessness in mathematics. (Indeed, most mathematicians continue working on problems as before.) What it means is that mathematical laws of a different kind might have to apply in certain situations: statistical laws. In the same way that it is impossible to predict the exact moment at which an individual atom undergoes radioactive decay, mathematics is sometimes powerless to answer particular questions. Nevertheless, physicists can still make reliable predictions about averages over large ensembles of atoms. Mathematicians may in some cases be limited to a similar approach.

84. Science Blog Research News In Science, Health, Medicine, Space
    diophantine equations - Dave Rusin s guide to diophantine equations. Linear diophantine equations - - A web tool for solving diophantine equations of  
    http://www.scienceblog.com/community/phpodp/odp.php?browse=/Science/Math/Number_

85. Diophantine Equation - Computing Reference - ELook.org
    Previous Terms, Terms Containing diophantine equation, Next Terms . DINO dinosaur dinosaur pen dinosaurs mating  
    http://www.elook.org/computing/diophantine-equation.htm

86. Avoiding Slack Variables In The Solving Of Linear Diophantine Equations And Ineq
    Avoiding Slack Variables in the Solving of Linear diophantine equations andInequations. Farid Ajili and Evelyne Contejean  
    http://www.lri.fr/~contejea/tcs97.html
    
    Extractions: In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, i.e. provides a (finite) description of the set of solutions, it can be implemented with a bounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm. full paper

87. Complete Solving Of Linear Diophantine Equations And Inequations Without Adding
    Complete Solving of Linear diophantine equations and Inequations without AddingVariables. Farid Ajili and Evelyne Contejean  
    http://www.lri.fr/~contejea/cp95.html
    
    Extractions: In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Contejean and Devie for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm of Fortenbacher for solving a single linear Diophantine equation. All the nice properties of the algorithm of Contejean and Devie are still satisfied by the new algorithm: it is complete, i.e. provides a (finite) description of the set of solutions, it can be implemented with a bounded stack, and it admits an incremental version. All of these characteristics enable its easy integration in the CLP paradigm. full paper

88. Solutions Of Diophantine Equations And Degree-one Polynomial Zeros Of Racah Coef
    Solutions of diophantine equations and degreeone polynomial zeros of Racahcoefficients. K Srinivasa Roa , V Rajeswari and RC King Inst. of Math.  
    http://www.iop.org/EJ/abstract/0305-4470/21/9/012
    
    Extractions: Print publication: Issue 9 (7 May 1988) Abstract. It is shown that the complete set of polynomial zeros of degree one of the Racah coefficients can be obtained only from the full eight-parameter solution of the multiplicative Diophantine equation: xyz=uvw subject to the constraint z=x+y+u+v+w. All other parametric solutions obtained are shown to represent only proper subsets of the complete set. doi:10.1088/0305-4470/21/9/012

89. Diophantine Equation--Linear
    PDF The diophantine equation Ax + By = Cz  
    http://hades.ph.tn.tudelft.nl/Internal/PHServices/Documentation/MathWorld/math/m

90. CMB - On The Diophantine Equation
    Previous Abstract Previous Page, On the diophantine equation n(n+d) (n+(k1)d)=byl, Next Page Next Abstract  
    http://www.journals.cms.math.ca/cgi-bin/vault/view/gyory8347

91. BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME DIOPHANTINE EQUATIONS
    BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME diophantine equationS Because ofthis famous result we call the above equation (1) the GoldbachVinogradov type  
    http://www.hku.hk/rss/res_proj/54/54.htm
    
    Extractions: BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME DIOPHANTINE EQUATIONS Prof. M.C. Liu Department of Mathematics HKU518/96P 1. STORY OF THE PROBLEM AND OUR MAIN RESULTS In 1967 A. Baker considered the Goldbach-Vinogradov type equation (1), where m and a j are certain integers and all p j are primes (i.e., prime numbers). When not all a a a are of the same sign (e.g., a 1 and a -1) he pioneered a series of deep problems. One of these is to obtain the best possible bound in terms of a a a and m for small prime solutions P P and P of the above equation (1). We call this problem the Baker Problem In fact, we obtained the best possible form for the bound of small prime solutions P P P of the above equation (1) with the numerical values of the constants in the bound unspecified. The essential part of the bound we obtained in 1989 is where B After our work of 1989, attention is focused on the value of the constant B since it is the last unknown as well as an essential part in the Baker Problem.

92. The Four Least Solutions In Distinct Positive Integers Of The Diophantine Equati
    http://www.cix.co.uk/~rosenstiel/cubes/welcome.htm
    
    Extractions: This article describes how one amateur number theorist with only limited computer experience (i.e., E. Rosenstiel) formed a team with two computer scientists to show that is the least solution in distinct positive integers of s q x y z w u v m n that the three next larger solutions are: and that the next one is greater than 5 x 10 . The paper ends with a brief survey of unsolved related problems. Introduction (E. Rosenstiel) T HIS project started when I was asked to write a program to list up to as high a limit as a simple microcomputer would permit all so called cubic doublets starting with which was already known in Euler's time as the least integer having two representations as the sum of two positive cubes. (In this century this "least doublet" entered mathematical folklore through Hardy's report of a visit to Ramanujan l in a Putney hospital via taxi cab No.1729.)

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