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         Diophantine Equation:     more books (59)
  1. Solutions of the Diophantine equation X² = DY=K, by Mohan Lal, 1968
  2. Diophantine equations by D Rameswar Rao, 1970
  3. Bounds for minimal solutions of diophantine equations (Nachrichten der Akademie der Wissenschaften in Gottingen, II. Mathematisch-Physikalische Klasse ; Jahrg. 1975, Nr. 9) by S Raghavan, 1975
  4. Contributions to the theory of a category of Diophantine equations of the second degree with two unknowns (Nova acta Regiae Societatis Scientiarum Upsaliensis, ser. 4, v. 16, n:o 2) by Trygve Nagell, 1955
  5. Diophantine equations and combinatorial identities obtained from units in quartic fields (Kent State University. Graduate College. Dissertations : Department of Mathematics) by Constantine K Kliorys, 1978
  6. Existence and representation of diophantine and mixed diophantine solutions to linear equations and inequalities by A Charnes, 1975
  7. The development and appraisal of a unit on Diophantine equations for prospective elementary school teachers by Tommy Harold Richard, 1971
  8. On polynomial time algorithms in the theory of linear Diophantine equations (Technical report / State University of New York at Buffalo, Department of Computer Science) by Eitan M Gurari, 1981
  9. The Farey series of order 1025 displaying solutions of the Diophantine equation bx - ay =: I, (Royal Society mathematical tables) by Eric Harold Neville, 1966
  10. Geometric Theorems, Diophantine Equations, and Arithmetic Functions by Jozsef Sandor, 2002-06
  11. On the diophantine equation y²-k=x³ by Ove Hemer, 1952
  12. Analytic methods for Diophantine equations and Diophantine inequalities;: [lecture notes] the University of Michigan, fall semester, 1962 by Harold Davenport, 1962
  13. Classical Diophantine Equations (Lecture Notes in Mathematics) by Vladimir G. Sprindzuk, 1994-02
  14. Diophantine equations and geometry by Fernando Quadros Gouvêa, 1987

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.,,2186,00.html
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 Google. Definition level 2.

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.
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.

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.

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

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.
Diploma Thesis
Algorithmic Solution of Diophantine Equations
(Stoll Thomas) ( ps
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.
thesis advisor: Tichy Robert, Dr.phil., O.Univ.-Prof.

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
From: Stephen Wolfram, A New Kind of Science
Notes for Chapter 12: The Principle of Computational Equivalence
Section: Implications for Mathematics and Its Foundations
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.)
Ever since antiquity there have been an increasing number of scattered results about Diophantine equations involving higher powers. In 1909

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
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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.
CWI Tract
CWI Tract 65
Algorithms for diophantine equations
by B.M.M. de Weger
order form order via WWW Comments to

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
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Diophantine Equations

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Diophantine Equations , a selection of answers from the Dr. Math archives.
Diophantine Equations
We have searched the Web for information about Diophantine equations.
Diophantine Equations, Step by Step
Find all positive integer solutions to 43x + 7y + 17z = 400.
Integer Solutions of ax + by = c
Given the equation 5y - 3x = 1, how can I find solution points where x and y are both integers? Also, how can I show that there will always be integer points (x,y) in ax + by = c if a, b and c are all integers?
Buying Cows, Pigs, and Chickens
A farmer buys 100 animals for $100. The animals include at least one cow, one pig, and one chicken. If a cow costs $10, a pig costs $3, and a chicken costs $0.50, how many of each did he buy?
How Many Mice, Cats, and Dogs?
You must spend $100 to buy 100 pets, choosing at least one of each pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00 each, and dogs @ $15.00 each. How many mice, cats, and dogs must you buy?
Money Puzzle
A man goes to the bank and asks for x dollars and y cents.

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).

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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 Associated Topics
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33. Title Details - Cambridge University Press
Home Catalogue Exponential diophantine equations. Related Areas Pure Mathematics.Exponential diophantine equations. TN Shorey, R. Tijdeman. £50.00.

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.

35. Diophantine Equation
diophantine equation. diophantine equations rational values. Examplesof diophantine equations are ax + by = 1 See B?out s identity.
Main Page See live article Alphabetical index
Diophantine equation
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
  • ax by = 1: See Bézout's identity x n y n z n : For n =2 there are many solutions ( x y z ), the Pythagorean triples. For larger values of n Fermat's Last Theorem states that no positive integer solutions x y z satisfying the above equation exist. x n y Pell's equation ) which is named, mistakenly, after the English mathematician John Pell. It was studied by Fermat
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.
This article is from Wikipedia . All text is available under the terms of the GNU Free Documentation License

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.
Diophantine Equations
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
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Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List 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).
Research Interests
Number Theory: - Diophantine Equations
- Subspace Theorem of W.M. Schmidt
- Diophantine m-Tuples Algebraic Geometry: - Algebraic Function Fields and Applications Coding Theory: - Geometric Goppa-Codes
- AG-Codes due to Xing, Niederreiter, Lam
Algebraisch-geometrische Codes , Diplomarbeit, TU Wien, 2000. ( dvi pdf Quantitative finiteness results for Diophantine equations, PhD-Thesis (Dissertation), TU Graz, 2002. ( dvi pdf
joint work with and R. F. Tichy Monatsh. Math.
Preprint: ( dvi pdf Diophantine m-tuples for linear polynomials, joint work with A. Dujella and R. F. Tichy Period. Math. Hungar.
Preprint: ( dvi pdf Perfect powers in linear recurring sequences, joint work with R. F. Tichy

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
Clemens Heuberger - Thue equations
Diophantine equations
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.
Thue equations
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).
Parametrized Thue equations
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.
The Free Online Dictionary of Computing ( Previous: diode Next: DIP
Diophantine equation
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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