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

Diophantine Equation by vasia reply to this message post a message on a new topic Back to sci.math.symbolic Subject: Diophantine Equation Author: aaa@bbb.com Date: 14 Jan 03 23:45:31 -0500 (EST) Does anybody know how to solve eq. in integers Axy + Bx + Cy = D Or how to prove that there are no solutions? This should be a known problem. I just dont know where to start. Thanks, - Vasia The Math Forum

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

Diophantine Equation by vaisa reply to this message post a message on a new topic Back to sci.math.num-analysis Subject: Diophantine Equation Author: aaa@bbb.com Date: 14 Jan 03 23:51:01 -0500 (EST) Does anybody know how to solve eq. in integers Axy + Bx + Cy = D Or how to prove that there are no solutions? This should be a known problem. I just dont know where to start. Thanks, - Vasia The Math Forum

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

Diophantine linear equation PROBLEM A.1,...,A.N T ALGORITHM My Diophant algorithm solves almost always diophantine equation for and IMPLEMENTATION Unit: internal subroutine Global variables: array A.1,...,A.N of positive integers Parameters: a positive integer N , a positive integer T Result: displays in the screen the solution of the problem - i. e. a subset A. whose sum is equal T . The execution is halted (via the exit statement) as soon as a solution is found Interface: internal procedure QUICKSORT DIOPHANT: procedure expose A. parse arg N, T call QUICKSORT N Ls.1 = A.1 do I = 2 to N Im1 = I - 1; Ls.I = A.I + Ls.Im1 end S = 1; Stack.1 = N T parse var Stack.S R T V; S = S - 1 if Ls.K = T then call EXIST V, K, 1 if A.R = T then call EXIST V, R, R D = V A.L; S = S + 1 Stack.S = (L - 1) (T - A.L) D end end end say "Solution not exist" exit EXIST: procedure expose A. parse arg V, B, E do J = B to E by -1; V = V A.J; end say "Solution:" V exit COMPARISON For N=100;T=25557 and the array A. created by statements: Seed = RANDOM(1, 1, 481989)

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

Diophantine equation An equation in which the coefficients are integers, and the solutions are also required to be integers. These equations often look deceptively simple and require difficult number theory to solve them. Find similar words More general: More specific: Defined earlier: Defined next: Ligning Linear Diophantine equation Number theory Pythagorean triple ... Pell's equation NRICH web-board archive Diophantine equation New search: Age: 19 Choose Language and Age Make a suggestion nrich@damtp.cam.ac.uk

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

Diophantine Equation What combination (number) of 21 coins (pennies, nickels and dimes) add up to one dollar? Solution Scroll to the answer. We have two equations. Let P represent the number of pennies, Let N represent the number of nickels, Let D represent the number of dimes. Since a penny is worth 1 cent, since a nickel is worth 5 cents and since a dime is worth 10 cents. 1P + 5N + 10D = 100 (the value of our coins) 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 D Number of Nickels N = Integer? no no no yes - 13 no no no yes - 4 no There are two answers. (1) 3 dimes, 13 nickels and 5 pennies (21 coins) have a value of one dollar (2) 7 dimes, 4 nickels and 10 pennies (21 coins) have a value of one dollar

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

Diophantine Equation Solve this Algebra equation for s and r s r Solution Scroll to the answer. There is a relationship between s and r but there is an unlimited number of possible r s combinations to satisfy the relationship. For any s (other than 2 - you can't get a product of 70 when one of the factors is zero, which also rules out r being -4), We will only be looking at integer answers. The prime factors of 70 are 2, 5 and 7, so 70 can be expressed as the following products: For any of these eight products, you can generate two possible solutions (except as noted). For example: Since 7 * 10 = 70, and s r + 4) = 70, then s - 2 = 7 and r + 4 = 10, or s = 9 and r Since 10 * 7 = 70, and s r + 4) = 70, then s - 2 = 10 and r + 4 = 7, or s = 12 and r Since there are eight ways to express 70 as the product of two factors, and two solutions for each factorization, there are 16 different integer answers. r s

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

Number Theory Diophantine Equations Diophantine Equation 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

6 citations found. Retrieving documents... Jones, J. Universal diophantine equation . Journal of Symbolic Logic 47 (1982), 549-571. Home/Search Document Not in Database Summary Related Articles Check 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

Please use a JavaScript-enabled browser! Get Microsoft Internet Explorer 4.0 for the best out of this site. For the meanwhile, you will have to use the text-based index to navigate the site. Sorry, JavaScript required for this. Genetic Algorithm Example: Diophantine Equation 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. Genetic Algorithm Example 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

Please use a JavaScript-enabled browser! 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. Genetic Algorithms: Diophantine Equation Solver 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: CDiophantine 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

The Free Online Dictionary of Computing ( http://foldoc.doc.ic.ac.uk/ dbh@doc.ic.ac.uk 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?]

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

Linear Diophantine Equation Solver Enter values for the equation below and press the button to solve for all x and y x y

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

Atlas Document # cacf-05 Turku Symposium on Number Theory in Memory of Kustaa Inkeri May 31 - June 4, 1999 University of Turku Turku, Finland Conference Organizers View Abstracts Conference Homepage On the Diophantine equation $(x^n - 1)/(x-1)=y^q$ presented by Yann Bugeaud We present a survey of recent results on the Diophantine equation (E) : (x n - 1)/(x-1) = y q - (E) has no solution with x being a square; - (E) has no solution (x, y, n, q) with n congruent to 1 modulo q, except (3, 11, 5, 2); Date received: February 3, 1999 The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc.

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

Atlas Document # cacf-05 Turku Symposium on Number Theory in Memory of Kustaa Inkeri May 31 - June 4, 1999 University of Turku Turku, Finland Organizers View Abstracts Conference Homepage On the Diophantine equation $(x^n - 1)/(x-1)=y^q$ by Yann Bugeaud We present a survey of recent results on the Diophantine equation (E) : (x n - 1)/(x-1) = y q - (E) has no solution with x being a square; - (E) has no solution (x, y, n, q) with n congruent to 1 modulo q, except (3, 11, 5, 2); Date received: February 3, 1999 Atlas Conferences Inc.

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

Previous: Tools page Up: Contents page SOLVE A DIOPHANTINE EQUATION In the fields below, enter the INTEGER coefficients of x and y and the constant term. Then click on the solve it button. Peter Williams Sat Oct 26 23:31:28 PDT 1996

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

RE:Diophantine equation From: Carol Toogood On: 4/20/1998 at 9:30 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

Asked NRICH NRICH Prime NRICH Club ... Get Printable Page March 03 Magazine Site Update News Events Problems Solutions ... Games Archive Problems Solutions Articles Inspirations ... Interactivities Web board Ask NRICH Asked NRICH NRICH Club Register Tough Nuts About Help! ... Where is NRICH? Associated Projects Maths Thesaurus MOTIVATE EuroMaths Millennium Maths ... Project Display maths using fonts images Help Back Issues Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 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 x Thanks By Gareth McCaughan on April 24, 1998 The possible values for x mod 13 are 0,1,5,8,12. The possible values for y mod 13 are 0,1,3,9, so the possible values for 2y are 0,2,6,5, so the possible values for 2y that are possible for the LHS and possible for the RHS, so there are no solutions to the equation mod 13.

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

Solution of a Diophantine Equation LPA Index Home Page

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