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

Home Contact Us Privacy Search 1Up Science Science A-Z A B C D ... Z Agriculture Animals Economics Farming Practices Field Crops ... More.. Alternative Science Alchemy Archaeology Astronomy Cryptozoology ... More.. Astronomy Astrophysics Calendars and Timekeeping Cosmology Eclipses and Occultations ... More.. Biology Biochemistry Biotechnology Botany Ecology ... More.. Chemistry Biochemistry Chemical Engineering Electrochemistry Elements ... More.. Earth Sciences Ecology Geology Geomatics Geophysics ... More.. Environment Air Quality Ecology Energy Health ... More.. Math Algebra Chaos and Fractals Differential Equations Geometry ... More.. Physics Alternative Astronomy Astrophysics Crystallography ... More.. Social Sciences Anthropology Archaeology Cognitive Science Economics ... Urban and Regional Planning s More.. Technology Acoustics Aerospace Chemical Engineering Electronics ... Number Theory : Diophantine Equations Description Categories Equal Sums of Like Powers Fermat's Last Theorem Other Languages Spanish Sites Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16: Fermat the integer set 1, 3, 8, 120.

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

Mathematical publications by Benjamin M.M. de Weger Home Book Papers Educational Books ... Lecture Notes Book Algorithms for diophantine equations CWI-Tract no. 65, Centre for Mathematics and Computer Science, Amsterdam [1989]. (MR 90m:11025, Zbl. 687.10013) Originally appeared as Ph.D. Dissertation, University of Leiden [1987]. Top of this page Papers Approximation lattices of p-adic numbers, Journal of Number Theory (MR 87k:11069, Zbl. 595.10027) Products of prime powers in binary recurrence sequences, Part I: The hyperbolic case, with an application to the generalized Ramanujan-Nagell equation, Mathematics of Computation (MR 87m:11027a, Zbl. 623.10011) Products of prime powers in binary recurrence sequences, Part II: The elliptic case, with an application to a mixed quadratic-exponential equation, Mathematics of Computation (MR 87m:11027b, Zbl. 623.10012) Solving exponential diophantine equations using lattice basis reduction algorithms, Journal of Number Theory (MR 88k:11097, Zbl. 625.10013) Erratum

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

Randomness in Arithmetic Scientific American 259, No. 1 (July 1988), pp. 80-85 by Gregory J. Chaitin 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

eLook Home eLook Computing Reference Search Computing Reference More Resources Information US City Data Worldwide Weather Entertainment Video Game Cheats Food Nutrition Recipes Literature Literature Reference Computing Dictionary Internet Encyclopedia Programming Reference ... Thesaurus By Letter: Non-alphabet A B C ... Z Diophantine equation integer coefficients to which integer solutions are sought. Because the results are restricted to integers, different algorithms must be used from those which find real solutions. [More details?] Terms Containing Diophantine equation DINO dinosaur dinosaur pen dinosaurs mating ... Contact

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

Avoiding Slack Variables in the Solving of Linear Diophantine Equations and Inequations Farid Ajili and Evelyne Contejean 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

Complete Solving of Linear Diophantine Equations and Inequations without Adding Variables Farid Ajili and Evelyne Contejean 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

@import url(http://ej.iop.org/style/nu/EJ.css); Quick guide Site map Athens login IOP login: Password: Create account Alerts Contact us Journals Home ... This issue K Srinivasa Roa et al J. Phys. A: Math. Gen. Solutions of Diophantine equations and degree-one polynomial zeros of Racah coefficients K Srinivasa Roa V Rajeswari and R C King Inst. of Math. Sci., Madras, India 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 URL: http://stacks.iop.org/0305-4470/21/1959 PDF (596 KB) References Articles citing this article Full text PDF (596 KB) References Articles citing this article Article options E-mail abstract Download to citation manager Link to this article Information about Filing Cabinet Find related articles By author K Srinivasa Roa V Rajeswari R C King IOP CrossRef Search Recommend Recommend this article Recommend this journal Author services NEW ... Submit referee report Reasons to login Set up an E-mail alert Use your Filing Cabinet Login Previous article ... Help Biomedical Materials British Journal of Applied Physics (1950-1967) Chinese Physics Chinese Physics Letters Classical and Quantum Gravity Clinical Physics and Physiological Measurement (1980-1992)

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

Diophantine EquationLinear A linear Diophantine equation (in two variables) is an equation of the general form where solutions are sought with , and Integers . Such equations can be solved completely, and the first known solution was constructed by Brahmagupta. Consider the equation Now use a variation of the Euclidean Algorithm , letting and Starting from the bottom gives so Continue this procedure all the way back to the top. Take as an example the equation Proceed as follows. The solution is therefore . The above procedure can be simplified by noting that the two left-most columns are offset by one entry and alternate signs, as they must since so the Coefficients of and are the same and Repeating the above example using this information therefore gives and we recover the above solution. Call the solutions to and . If the signs in front of or are Negative , then solve the above equation and take the signs of the solutions from the following table: equation In fact, the solution to the equation is equivalent to finding the Continued Fraction for , with and Relatively Prime (Olds 1963). If there are

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

n(n+d) ... (n+(k-1)d)=by l CMB (2004) Vol 47 No 3 / pp. 373-388 On the Diophantine Equation n(n+d) ... (n+(k-1)d)=by l Abstract TeX format n,y when b=d=1 . We show that there are only finitely many solutions in n,d,b,y when are fixed and For download Keywords none Language English Category Primary: 11D41 Secondary: none

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

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

The Four Least Solutions in Distinct Positive Integers of the Diophantine Equation s x y z w u v m n E. ROSENSTIEL, MDS, London J. A. DARDIS, AFIMA University of London Computer Centre and C. R. ROSENSTIEL Cambridge [From The Institute of Mathematics and its Applications Bulletin July, 1991, Volume 27, pp 155-157 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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