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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. Mathsoft: Mathsoft Unsolved Problems: On A Generalized Fermat-Wiles Equation
    Steven Finch's essay on the diophantine equation of the form x^n + y^n = c.z^n.  
    http://www.mathsoft.com/mathresources/problems/article/0,,2186,00.html
    
    Extractions: search site map about us  + news  + ... Unsolved Problems Links On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos Mathsoft Constants Engineering Standards ... Math Resources On a Generalized Fermat-Wiles Equation Fermat's Last Theorem was no more than a conjecture for over 350 years. Let n be an integer greater than 2. Fermat claimed that any integers x, y and z, not necessarily positive, for which x n + y n = z n To some people, the passage of this conjecture to theoremhood is marked by sadness. They may mistakenly believe that no other interesting Diophantine equations are left to be solved. This essay is aimed at such individuals: there is a much larger class of equations, of which Fermat-Wiles is only a special case, that is well worth everyone's attention! The equation we'll examine is x n + y n n where c is a positive integer. We wish to learn what conditions on n and c force the existence of a non-trivial 0. In other words, when is the equation x n + y n n solvable x + y Click here for more terms The infinite sequence of all such integers c can be shown to be highly sparse relative to the sequence of positive integers. By the

22. LinearDiophantineEquation
    Linear diophantine equation (English). Search for Linear Diophantineequation in NRICH PLUS maths.org Google. Definition level 2.  
    http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=888

23. The Beal Conjecture
    $75,000 prized problem pertaining to the diophantine equation of the form A^x + B^y = C^z where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common factor.  
    http://www.math.unt.edu/~mauldin/beal.html
    
    Extractions: BEAL'S CONJECTURE: If A x +B y = C z , where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. THE BEAL PRIZE. The conjecture and prize was announced in the December 1997 issue of the Notices of the American Mathematical Society. Since that time Andy Beal has increased the amount of the prize for his conjecture. The prize is now this: $100,000 for either a proof or a counterexample of his conjecture. The prize money is being held by the American Mathematical Society until it is awarded. In the meantime the interest is being used to fund some AMS activities and the annual Erdos Memorial Lecture. CONDITIONS FOR WINNING THE PRIZE. The prize will be awarded by the prize committee appointed by the American Mathematical Society. The present committee members are Charles Fefferman, Ron Graham, and Dan Mauldin. The requirements for the award are that in the judgment of the committee, the solution has been recognized by the mathematics community. This includes that either a proof has been given and the result has appeared in a reputable refereed journal or a counterexample has been given and verified. PRELIMINARY RESULTS.

24. Diophantine Equation
    diophantine equation. Introduction. A diophantine equation is an equation in which only Integer solutions are allowed. Hilbert's 10th Problem asked if a technique for solving a general Diophantine existed.  
    http://granite.sru.edu/~venkatra/Diophantine_Equation.htm

25. The Prime Glossary: Diophantus
    Now we call an equation to be solved in integers a diophantine equation.For example, Diophantus considered the equations ax + by = c.  
    http://primes.utm.edu/glossary/page.php?sort=Diophantus

26. Diophantine Equation
    diophantine equation A diophantine equation is an equation for which the solutions are required to be integers. Generally, solving a diophantine equation is not as straightforward as solving a  
    http://rdre1.inktomi.com/click?u=http://planetmath.org/encyclopedia/DiophantineE

27. Diploma Thesis
    Stoll Thomas) (ps) The diophantine equation X^MY^N=1, known as Catalan s equation,can well be treated with Baker s theory of linear forms in logarithms.  
    http://finanz.math.tugraz.at/~stoll/diplthesis.htm
    
    Extractions: The Diophantine equation X^M-Y^N=1, known as Catalan's equation, can well be treated with Baker's theory of linear forms in logarithms. In detail, we give both Baker's proof of his general transcendence result and Tijdeman's proof on Catalan's equation, which gives an explicit upper bound for max(x,y,m,n). This method for showing effective finiteness also works for elliptic and hyperelliptic equations. In the thesis much emphasize is laid on the decidability of non-effective finiteness of the more general Diophantine equation F(X)=G(Y), F and G being arbitrary polynomials. Recent progress has been made by Bilu and Tichy in showing that, by making explicit Siegel's theorem, these polynomials have to satisfy polynomial identities with the o-called standard pairs. In the sequel, an algorithmic implementation of such criterion is given as a Maple worksheet. We study the case, where F and G belong to a polynomial family. For this reason we include a general approach to define orthogonal polynomials and state the fundamental properties they all have in common. In the case where F and G are Meixner polynomials of fixed degree, we prove that there are only finitely many integral solutions (X,Y) to F(X)=G(Y). Geometrically speaking, two octahedrons of dimensions N and M, respectively, can have equally many integral points just in a finite number of cases.

28. Historical Notes: Diophantine Equations
    Particularly from the work of Carl Friedrich Gauss around 1800 there emergeda procedure to find solutions to any quadratic diophantine equation in two  
    http://www.wolframscience.com/reference/notes/1164b
    
    Extractions: Diophantine equations. If variables appear only linearly, then it is possible to use ExtendedGCD (see page 946) to find all solutions to any system of Diophantine equations - or to show that none exist. Particularly from the work of Carl Friedrich Gauss around 1800 there emerged a procedure to find solutions to any quadratic Diophantine equation in two variables - in effect by reduction to the Pell equation x^2==a y^2+1 (see page 947), and then computing ContinuedFraction[Sqrt[a]]. The minimal solutions can be large; the largest ones for successive coefficient sizes are given below. (With size s coefficients it is for example known that the solutions must always be less than (14 s)^(5s).). There is a fairly complete theory of homogeneous quadratic Diophantine equations with three variables, and on the basis of results from the early and mid-1900s a finite procedure should in principle be able to handle quadratic Diophantine equations with any number of variables. (The same is not true of simultaneous quadratic Diophantine equations, and indeed with a vector x of just a few variables, a system m . x^2 == a of such equations could quite possibly show undecidability.)

29. Stephen Wolfram: A New Kind Of Science | Online
    diophantine equations. Any algebraic b. Even the simplest quadratic Diophantineequations can already show much more complex behavior. The  
    http://www.wolframscience.com/nksonline/page-944f-text

30. CWI Tract
    CWI Tract 65. Algorithms for diophantine equations. by BMM de Weger. Then it becomesfeasible to determine all the solutions of the original diophantine equation.  
    http://www.cwi.nl/publications/Abstracts_tracts/tr-65.html

31. Math Forum - Ask Dr. Math Archives: Diophantine Equations
    Linear diophantine equation Given positive integers a and b such that a b^2,b^2 a^3, a^3 b^4, b^4 a^5, . prove that a = b. Solving Multivariable  
    http://mathforum.org/library/drmath/sets/select/dm_diophantine.html

32. Math Forum - Ask Dr. Math
    A diophantine equation is one equation in at least two variables, say x andy, whose solutions (x,y) are required to be whole numbers (integers).  
    http://mathforum.org/library/drmath/view/54241.html
    
    Extractions: Associated Topics Dr. Math Home Search Dr. Math Date: 11/17/97 at 15:37:25 From: Robert Felgate Subject: Diaphantine equations Dear Dr. Math, We have been investigating Pythagoras' theorem, and our teacher has suggested we search the web for information about diaphantine equations. We have not been very successful and wonder if you would help us. Thank you. Robert and his Mum http://mathforum.org/dr.math/ Associated Topics

33. Title Details - Cambridge University Press
    Home Catalogue Exponential diophantine equations. Related Areas Pure Mathematics.Exponential diophantine equations. TN Shorey, R. Tijdeman. £50.00.  
    http://titles.cambridge.org/catalogue.asp?isbn=0521268265

34. Title Details - Cambridge University Press
    Home Catalogue diophantine equations over Function Fields. Related Areas PureMathematics. diophantine equations over Function Fields. RC Mason. £16.99.  
    http://titles.cambridge.org/catalogue.asp?isbn=0521269830

35. Diophantine Equation
    diophantine equation. diophantine equations rational values. Examplesof diophantine equations are ax + by = 1 See B?out s identity.  
    http://www.fact-index.com/d/di/diophantine_equation.html
    
    Extractions: Main Page See live article Alphabetical index Diophantine equations are equations of the form f = 0, where f is a polynomial with integer coefficients in one or several variables which take on integral values. They are named after Diophantus who studied equations with variables which take on rational values. Examples of Diophantine equations are The depth of the study of general Diophantine equations is shown by the characterisation of Diophantine sets as recursively enumerable The field of Diophantine approximation deals with the cases of Diophantine inequalities : variables are still supposed to be integral, but some coefficients may be irrational numbers, and the equality sign is replaced by upper and lower bounds.

36. Diophantine Equations -- From Eric Weisstein's Encyclopedia Of Scientific Books
    diophantine equations. see also diophantine equation. Bashmakova, Isabella Grigoryevna.Diophantus and diophantine equations. Washington, DC Math.  
    http://www.ericweisstein.com/encyclopedias/books/DiophantineEquations.html
    
    Extractions: see also Diophantine Equation Bashmakova, Isabella Grigoryevna. Diophantus and Diophantine Equations. Washington, DC: Math. Assoc. Amer., 1997. 104 p. $21.95. Beiler, A.H. Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. New York: Dover, 1966. A great place to start learning number theory. Well worth the modest price. $7.95. Carmichael, Robert Daniel. The Theory of Numbers, and Diophantine Analysis. New York: Dover, 1959. An unabridged and unaltered republication of the two works, originally published separately. Out of print. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 96-104, 1965. $7.95. Hardy, G.H. and Wright, E.M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979. $42.95. Hunter, J.A.H. and Madachy, J.S. ``Diophantos and All That.'' Ch. 6 in Mathematical Diversions. New York: Dover, pp. 52-64, 1975. $5.95. Ireland, K. and Rosen, M. ``Diophantine Equations.'' Ch. 17 in A Classical Introduction to Modern Number Theory, 2nd ed.

37. PlanetMath: Diophantine Equation
    diophantine equation, (Definition). A diophantine equation is an equationfor which the solutions are required to be integers. Generally  
    http://planetmath.org/encyclopedia/DiophantineEquation.html
    
    Extractions: Diophantine equation (Definition) A Diophantine equation is an equation for which the solutions are required to be integers Generally, solving a Diophantine equation is not as straightforward as solving a similar equation in the real numbers . For example, consider this equation: It is easy to find real numbers that satisfy this equation: pick any arbitrary and , and you can compute a from them. But if we require that all be integers, it is no longer obvious at all how to find solutions. Even though raising an integer to an integer power yields another integer, the reverse is not true in general. As it turns out, of course, there are no solutions to the above Diophantine equation: it is a case of Fermat's last theorem At the Second International Congress of Mathematicians in 1900, David Hilbert presented several unsolved problems in mathematics that he believed held special importance. Hilbert's tenth problem was to find a general procedure for determining if Diophantine equations have solutions:

38. Research.html
    (dvi, pdf). On the diophantine equation G_ {n}(x)=G_{m}(P(x)), joint work with A.Pethõ and RF Tichy, Monatsh. Math. 137 (2002) 3, 173196 Preprint (dvi, pdf).  
    http://finanz.math.tu-graz.ac.at/~fuchs/research.html

39. Clemens Heuberger - Thue Equations
    Among his 23 Problems, Hilbert raised the question, whether there exists an algorithmto solve any given polynomial diophantine equation; the negative answer  
    http://finanz.math.tu-graz.ac.at/~cheub/thue.html
    
    Extractions: Since antiquity, many people try to solve equations over the integers, Pythagoras for instance described all integers being the sides of a rectangular triangle. After Diophantus von Alexandrien such equations are called diophantine equations . Since that time, many mathematicians worked on this topic, such as Fermat, Euler, Kummer, Siegel, and Wiles. Among his 23 Problems, Hilbert raised the question, whether there exists an algorithm to solve any given polynomial diophantine equation; the negative answer has been given by Matijasevic in 1970. So the research interest in diophantine equations is to find classes of such equations which can be solved. In 1909, A. Thue considered a special family of equations F(X,Y) = m, where F is an irreducible homogeneous form of degree n at least 3 and m is a nonzero integer. This type of equations is called after him since then; he proved that such an equation only has a finite number of solutions. His proof, however, is not constructive, so it does not lead to an algorithm. Only with Baker's lower bounds for linear forms in logarithms of algebraic numbers (19661968), effective bounds for the solution of many diophantine equations can be given. Since that time, many bounds have been improved and algorithms have been developed to solve one single Thue-equation in reasonable time on a computer (see Bilu and Hanrot). In 1990, E. Thomas studied a parametrized family of cubic Thue equations: It turns out that there exist only a few "trivial" solutions for large values of the parameter.

40. 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?]

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