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Diophantine Equation:     more books (88)

Logic, Methodology and Philosophy of Science Proceedings of the 1960 International Conference by J. Richard Buchi, Julia Robinson, et all 1965 Geometric Theorems, Diophantine Equations, and Arithmetic Functions (second edition) by Jozsef Sandor, 2008-10-11 Diophantine Equations: Pythagorean Triple The Farey series of order 1025,displaying solutions of the Diophantine equation bx-ay=1 (Royal Society mathematical tables series;vol.1) by Eric Harold Neville, 1950 Diophantus and Diophantine Equations by Isabella Bashmakova, 2009-01-01 Polynomial Diophantine Equation An Introduction to Diophantine Equations by Andreescu/Andrica, 2002 Diophantus and Diophantine equations / Diofant i diofantovy uravneniya by Bashmakova I.G., 2007 Diophantine Equations (Berichte Aus Der Mathematik) by Uwe Kraeft, 2000-11-08 Diophantine Equations (Studies in Mathematics) by N. Saradha, 2008-05-06 Representations of Primes By Quadratic Forms Displaying Solutions of the Diophantine Equation : Royal Society Mathematical Tables Volume 5 by Hansraj ; Cheema, M. S. ; Mehta, A.; Gupta, O. P. ; Miller, J. C. P. (edi Gupta, 1960-01-01 Diophantine equations and provability in mathematics / Diofantovy uravneniya i dokazuemost v matematike by Moroz, 2008 Number Theory Unit 8: Diophantine Equations (Course M381) by Alan Best, 1996-12-01 Diophantine Approximation and Diophantine Equations by Wolfgang M. Schmidt, 1990

lists with details

21. Diophantine Equation By Vasia
    diophantine equation by vasia. Subject diophantine equation Author vasia aaa@bbb.com Date 14 Jan 03 234531 0500 (EST) Does anybody know how to solve eq.  
    http://mathforum.org/epigone/sci.math.symbolic/strimglaldben

22. Diophantine Equation By Vaisa
    diophantine equation by vaisa. Subject diophantine equation Author vaisa aaa@bbb.com Date 14 Jan 03 235101 0500 (EST) Does anybody know how to solve eq.  
    http://mathforum.org/epigone/sci.math.num-analysis/phyblelfrerd

23. Diophantine Equation
    Diophantine linear equation. ALGORITHM My Diophant algorithm solvesalmost always diophantine equation for N =500 and AI =2*10**9.  
    http://www.geocities.com/zabrodskyvlada/aat/a_diop.html

24. Maths Thesaurus: Diophantine Equation
    Home diophantine equation An equation in which the coefficients are integers,and the solutions are also required to be integers. diophantine equation.  
    http://thesaurus.maths.org/dictionary/map/word/967

25. Diophantine Equation
    diophantine equation What combination (number) of 21 coins (pennies, nickelsand dimes) add up to one dollar? Solution. Scroll to the answer.  
    http://westview.tdsb.on.ca/Mathematics/sc/diophantine.equation2.html
    
    Extractions: P + N + D = 21 (the number of coins) Which we can re-write as P = 21 - N - D Substitute this into "the value of our coins" equation we get: (21 - N - D) + 5N + 10D = 100 or There are many different possible answers but we are only interested in whole number solutions. Substsitute 0, 1, 2, 3, 4, 5, 6, 7, 8 for D and solve for whole number solutions for N. Number of Dimes

26. Diophantine Equation
    diophantine equation Solve this Algebra equation for s and r (s 2)(r+4) = 70. Solution. Scroll to the answer. There is a relationship  
    http://westview.tdsb.on.ca/Mathematics/sc/diophantine.equation.html

27. Diophantine Equation -- From MathWorld
    Similar pages An Algorithm for Solving a diophantine equation With Lower And We develop an algorithm for solving a diophantine equation with lower and upperbounds on the variables. An Algorithm for Solving a diophantine equation With  
    http://www.astro.virginia.edu/~eww6n/math/DiophantineEquation.html
    
    Extractions: An equation in which only integer solutions are allowed. Hilbert's 10th problem asked if a technique for solving a general Diophantine existed. A general method exists for the solution of first degree Diophantine equations. However, the impossibility of obtaining a general solution was proven by Julia Robinson and Martin Davis in 1970, following proof of the result that the relation (where is a Fibonacci number ) is Diophantine by Yuri Matiyasevich (Matiyasevich 1970, Davis 1973, Davis and Hersh 1973, Davis 1982, Matiyasevich 1993). More specifically, Matiyasevich showed that there is a polynomial P in n m , and a number of other variables x y z , ... having the property that iff there exist integers x y z , ... such that Jones and Matiyasevich (1982) proved that no algorithms can exist to determine if an arbitrary Diophantine equation in nine variables has solutions. As a consequence of this result, it can be proved that there does not exists a general algorithm for solving a quartic Diophantine equation , although the algorithm for constructing such an unsolvable quartic Diophantine equation can require arbitrarily many variables (Matiyasevich 1993).

28. Citations: Universal Diophantine Equation - Jones (ResearchIndex)
    Retrieving documents Jones, J. Universal diophantine equation. Journal of SymbolicLogic 47 (1982), 549571. Jones, J. Universal diophantine equation.  
    http://citeseer.nj.nec.com/context/220874/0
    
    Extractions: This paper is cited in the following contexts: Termination of Term Rewriting - Zantema (2000) (2 citations) (Correct) ....(a n ) 0) in the last line the conjunction runs over all 2 choices of f i being either X or 4 X for i = 1; n. By applying the assumed decision procedure on all of these 2 conjuncts this yields a decision procedure for Hilbert s tenth problem, contradiction. 2 According to Hilbert s tenth problem is even undecidable if only polynomials in n 9 variables are considered. Since the number of variables is preserved by the construction in the proof of Proposition 11, it also holds for polynomials in n 9 variables. But also for polynomials of a low degree in far less .... Jones, J. Universal diophantine equation . Journal of Symbolic Logic 47 (1982), 549-571. Toric Laminations, Sparse Generalized Characteristic Polynomials.. - Rojas (1997) (Correct) ....the rather surprising fact that restructuring Hilbert s Tenth Problem as the union S 1 d=0 Hilb(d) seems to be new. In particular, Hilbert s Tenth Problem was originally stated as deciding the existence of a single integral root for one polynomial in several variables.

29. Diophantine Equation From FOLDOC
    Online Computing Dictionary. Register a Domain. diophantine equation. mathematics Equations with integer coefficients to which integer solutions are sought.  
    http://www.instantweb.com/D/dictionary/foldoc.cgi?Diophantine equation

30. Generation 5: Artificial Intelligence Repository - Genetic Algorithm Example: Di
    Sorry, JavaScript required for this. Genetic Algorithm Example DiophantineEquation. Genetic Algorithm Example diophantine equation.  
    http://hyperion.advanced.org/18242/gaexample.shtml
    
    Extractions: For the meanwhile, you will have to use the text-based index to navigate the site. Sorry, JavaScript required for this. Make sure that you have read the genetic algorithms essay before reading this example. You also must have a working knowledge of C++ and object-oriented programming to utilize the classes and code examples provided. Let us consider a diophantine (only integer solutions) equation: a+2b+3c+4d=30 , where a,b,c,d are positive integers. Using a genetic algorithm, all that is needed is a little time to reach a solution (a,b,c,d) . Of course you could ask, why not just use a brute force method (plug in every possible value for a,b,c,d given the constraints < a,b,c,d = )? The architecture of GA systems allow for a solution to be reached quicker since "better" solutions have a better chance of surviving and procreating, as opposed to randomly throwing out solutions and seeing which ones work. Let's start from the beginning. First we will choose 5 random initial solution sets, with constraints

31. Generation 5 Artificial Intelligence Repository - Genetic
    Genetic Algorithms diophantine equation Solver. This is a C++ programthat solves a diophantine equation using genetic algorithms.  
    http://hyperion.advanced.org/18242/diophantine_ga.shtml
    
    Extractions: Get Microsoft Internet Explorer 4.0 for the best out of this site. Use the Text-based Index to navigate the site. Sorry, JavaScript required for this. This is a C++ program that solves a diophantine equation using genetic algorithms. This is the first program is a new set of programs popping up on Generation5 - case studies. Therefore this page is a huge break down of the code and what it does, how it does it, and how to use it. Without further ado, here is the download link: diophantine.zip This code is the accompanying code to the genetic algorithms example , so please read that if you don't know anything about GAs before attempting to look at this code. Trust me, Sam wrote the essay, and I learnt and coded the program straight from what I learnt from that essay - its great! Now for the code: Firstly the class header (note for formatting reasons, a lot of the documentation is taken out): Firstly you notice that there are two structures, the gene structure and the actual CDiophantine class. The gene structure is used to keep track of the different solution sets. The population generated is a population of genes. The gene structure keeps track of its own fitness and likelihood values itself. I also coded a small function to test for equality, this just made some other code a lot more concise. Now onto the functions.

32. Diophantine Equation
    Previous diode Next DIP. diophantine equation. mathematics Equationswith integer coefficients to which integer solutions are sought.  
    http://burks.brighton.ac.uk/burks/foldoc/28/32.htm
    
    Extractions: The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk Previous: diode Next: DIP mathematics 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?]

33. Diofantos, Diophantos, Diophantine Equation, Diofantoksen
    With this applet you can solve the linear diophantine equation. Tälläsovelmalla voi ratkaista lineaarisen Diofantoksen yhtälön.  
    http://www.kolumbus.fi/hoijer.heikki/Diofantos.html

34. Linear Diophantine Equation Solver
    Linear diophantine equation Solver. Enter values for the equationbelow and press the button to solve for all x and y x, +, y, =,  
    http://www.student.math.uwaterloo.ca/~madrewbr/lde.html

35. Atlas: On The Diophantine Equation $(x^n - 1)/(x-1)=y^q$ By Yann Bugeaud
    On the diophantine equation $(x^n 1)/(x-1)=y^q$ presented by Yann BugeaudUniversité Louis Pasteur IRMA 7, rue Descartes 67084 STRASBOURG (FRANCE)  
    http://atlas-conferences.com/c/a/c/f/05.htm

36. Atlas: On The Diophantine Equation $(x^n - 1)/(x-1)=y^q$ Presented By Yann Bugea
    On the diophantine equation $(x^n 1)/(x-1)=y^q$ by Yann Bugeaud UniversitéLouis Pasteur IRMA 7, rue Descartes 67084 STRASBOURG (FRANCE)  
    http://atlas-conferences.com/cgi-bin/abstract/cacf-05

37. SOLVE A DIOPHANTINE EQUATION
    previous up Previous Tools page Up Contents page. SOLVE A DIOPHANTINEEQUATION. In the fields below, enter the INTEGER coefficients  
    http://www.math.csusb.edu/notes/maple/plot/dioph.html

38. RE:Diophantine Equation
    REdiophantine equation. FromCarol Toogood On4/20/1998 at 930Prove there are no integer solutions to x 3 =2y 4 + 17 I need a  
    http://www.nrich.maths.org.uk/mathsf/journalf/aams/q60.html
    
    Extractions: Prove there are no integer solutions to x + 17 I need a review of techniques( using mod operations) to solve this sort of question. Please start at the beginning as I am very rusty on Number theory Thanks (t314) From: Gareth McCaughan On: 4/24/1998 at 15:01 So: the sort of thing you can do here is to look at the equation modulo various prime numbers and try to show that there aren't any solutions mod p for some cleverly chosen p. (`Cleverly chosen' in practice means: you try several, and if you hit one that works you pretend it was the first one you thought of.) This has some chance of success because for suitable p only about 1/3 of residues are cubes and for other suitable p only about 1/4 of residues are 4th powers. Specifically, if p is 1 (mod 3) then there aren't very many cubes mod p; if p is 1 (mod 4) then there aren't very many fourth powers mod p. So maybe we should try p=13, since that meets both criteria. The possible values for x mod 13 are 0,1,5,8,12. The possible values for y

39. NRICH Mathematics Enrichment Club (1293.html)
    diophantine equation By Carol Toogood (t314) on April 20, 1998 Provethere are no integer solutions to x 3 =2y 4 + 17 I need a  
    http://www.nrich.maths.org.uk/askedNRICH/edited/1293.html
    
    Extractions: Bernard's Bag(P) - solutions(P) Penta Probs(P) - solutions(P) Let Me Try(P) - solutions(P) Kid's Mag(P) Play Games(P) Staff Room(P) 6 Problems - solutions 15+Challenges - solutions Articles Games LOGOland Editorial News Diophantine equation By Carol Toogood (t314) on April 20, 1998 Prove there are no integer solutions to

40. Solution Of A Diophantine Equation
    Solution of a diophantine equation. % dioph(+A, +B, +C, ?X0, ?Y0)is true if x = X0 + B * n and % y = Y0 A * n (for any integer  
    http://perso.wanadoo.fr/colin.barker/lpa/dioph.htm

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