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Diophantine Equation:     more books (88)

Two-way counter machines and diophantine equations (Technical report / State University of New York at Buffalo, Department of Computer Science) by Eitan M Gurari, 1980 Representations of primes by quadratic forms: Displaying solutions of the Diophantine equation kp=a²+Db² (Royal Society mathematical tables) by Hansraj Gupta, 1960 Diophantine equations by D Rameswar Rao, 1970 On the diophantine equation y²-k=x³ by Ove Hemer, 1952 Tables of solutions of the diophantine equation x² + y² + z² = k² by Mohan Lal, 1967 The Farey series of order 1025 displaying solutions of the Diophantine equation bx - ay =: I, (Royal Society mathematical tables) by Eric Harold Neville, 1966 Diophantine equations and geometry by Fernando Quadros Gouvêa, 1987 Tables of solutions of the diophantine equation Y3 - X2 =: K by Mohan Lal, 1965 Diophantus and Diophantine Equations by Isabella G. Bashmakova, 1998 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 Certain quaternary quadratic forms and diophantine equations by generalized quaternion algebras by Lois Wilfred Griffiths, 1927 Diophantine equations, with special reference to elliptic curves by J. W. S Cassels, 1966 Diophantine equations: A p-adic approach by Wilhelm Ljunggren, 1968 A note on the solvability of the diophantine equation: 1n [superscript n] + 2n [superscript n] + ... mn [superscript n] = G(m+1)n [superscript n] (Afdeling zuivere wiskunde) by J. van de Lune, 1975

lists with details

61. Number Theory: Diophantine Equations
    Developing A General 2nd Degree diophantine equation x^2 + p = 2^n. Methodsto solve these equations. Quadratic diophantine equation Solver.  
    http://www.puredirectory.com/Science/Math/Number-Theory/Diophantine-Equations/
    
    Extractions: Home Science Math Number Theory : Diophantine Equations Equal Sums of Like Powers Fermat's Last Theorem google_ad_client = "pub-3272565765518472";google_alternate_color = "FFFFFF";google_ad_width = 336;google_ad_height = 280;google_ad_format = "336x280_as";google_ad_channel ="7485447737";google_color_border = "FFFFFF";google_color_bg = "FFFFFF";google_color_link = "0000FF";google_color_url = "008000";google_color_text = "000000"; Standard Listings

62. 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

63. Maths Glossary
    diophantine equation An equation which is required to be solved by integers.Thusthe diophantine equation 2x 2 3y 2 = 5 has the integer solution x=2,y=1  
    http://www.fortunecity.com/emachines/e11/86/mathglos.html
    
    Extractions: Complex Number : A 2 dimensional number comprising a real and imaginary component of the form A+Bi,where i is the square root of -1.Such numbers are mapped on the Argand plane and form a matrix of numbers,the imaginary numbers being at right angles to the real ones.The conjugate takes the form a-bi. Continuum Hypothesis : In Cantorian set theory,the cardinal number of a set designates its "manyness". The cardinality of the set of integers 1,2,3,... is designated by .The cardinality of the set of real numbers is 2 .The continuum hyopothesis asserts that there is no set whose cardinal falls between and 2

64. Generation5 - Genetic Algorithm Example: Diophantine Equation
    Home Articles Genetic Algorithms Beginner Genetic Algorithm Example DiophantineEquation By Samuel Hsiung and James Matthews, Printable Version.  
    http://www.gamedev.net/reference/articles/article560.asp
    
    Extractions: By Samuel Hsiung and James Matthews Printable Version 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

65. :: Ez2Find :: Diophantine Equations
    URL http//liinwww.ira.uka.de/bibliography/Math/Hilbert10.html; Developing A General2nd Degree diophantine equation x^2 + p = 2^n Site Info - Translate  
    http://ez2find.com/cgi-bin/directory/meta/search.pl/Science/Math/Number_Theory/D
    
    Extractions: Any Language English Afrikaans Arabic Bahasa Melayu Belarusian Bulgarian Catala Chinese Simplified Chinese Traditional Cymraeg Czech Dansk Deutsch Eesti Espanol Euskara Faroese Francais Frysk Galego Greek Hebrew Hrvatski Indonesia Islenska Italiano Japanese Korean Latvian Lietuviu Lingua Latina Magyar Netherlands Norsk Polska Portugues Romana Russian Shqip Slovensko Slovensky Srpski Suomi Svenska Thai Turkce Ukrainian Vietnamese Mode

66. Applicatons - Solve Diophantine Equations
    Instructions This function will enable one to find all integer solutionsto the above equation, also known as a diophantine equation.  
    http://archives.math.utk.edu/articles/atuyl/confrac/diaph.html
    
    Extractions: A * X + B * Y = C where a,b, and c are given, non-zero integers Instructions: This function will enable one to find all integer solutions to the above equation, also known as a Diophantine equation In the space provided below enter the integer values of A,B, and C. When this is completed, press the bar below. The value of A: The value of B: The value of C: Main Introduction History Applications ... Credits

67. ThinkQuest : Library : Generation 5: The Artificial Intelligence Repository
    Sorry, JavaScript required for this. Genetic Algorithm Example DiophantineEquation. Genetic Algorithm Example diophantine equation.  
    http://library.thinkquest.org/18242/gaexample.shtml
    
    Extractions: Index Artificial Intelligence Will computers be able to function without humans in the future? This entry on Artificial Intelligence explores the history of AI and tells us what to look forward to in the future. Interviews with important people in the field are included. Various essays present topics such as Introduction to Natural Language Processing, Neural Networks, and Robotics. Visit Site 1998 ThinkQuest Internet Challenge Languages English Spanish German French Students Sam Lincoln Park Highschool, Chicago, IL, United States Edward Clear Lake High School, Houston, TX, United States Coaches Michael Clear Lake High School, Houston, TX, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

68. Mathematical Programming Glossary Page 2
    diophantine equations. A system of equations whose variables mustbe integervalued. A famous one is in Fermat s Last Theorem x  
    http://carbon.cudenver.edu/~hgreenbe/glossary/second.php?page=D.html

69. Generation5 - Diophantine Equation Solver
    diophantine equation Solver By James Matthews, Printable Version. This is aC++ program that solves a diophantine equation using genetic algorithms.  
    http://www.generation5.org/content/2000/diophantine_ga.asp

70. Diophantine Equations In Naturals -- References
    and Tomás, 1995 Miguel Filgueiras and Ana Paula Tomás, A fast method for findingthe basis of nonnegative solutions to a linear diophantine equation.  
    http://www.ncc.up.pt/~apt/dioph/hdioph_1.html
    
    Extractions: References Ana Paula, On Solving Linear Diophantine Constraints . Doctoral thesis, Universidade do Porto, 1997. and Filgueiras, 1997a] Proceedings of 8th Conference on Rewriting Techniques and Applications RTA'97 , Lecture Notes in Computer Science 1232, 269-283, Springer-Verlag,1997. Reviewed in Math Reviews and Filgueiras, 1997b] Progress in Artificial Intelligence EPIA'97 , Lecture Notes in Artificial Intelligence 1323, 73-84, Springer-Verlag, 1997. Reviewed in , 884.11020; (Reviewer J. Piehler) 11D04, 90C10. [Filgueiras Journal of Symbolic Computation , 19, 507-526, 1995. Reviewed in Math Reviews [Filgueiras Progress in Artificial Intelligence 6th Portuguese Conference on Artificial Intelligence , Lecture Notes in Artificial Intelligence 727, 297-306, Springer-Verlag, 1993. Reviewed in Math Reviews and Filgueiras, 1991a] Proceedings of the 5th Portuguese Conference on Artificial Intelligence , Lecture Notes in Artificial Intelligence 541, Springer-Verlag, 30-44, 1991. and Filgueiras, 1997c] COMPULOG NET Workshop on Constraint Programming and Filgueiras, 1993]

71. Lukol Directory - Science Math Number Theory Diophantine Equations
    Hilbert s Tenth Problem Given a diophantine equation with any number of unknownsand with rational integer coefficients devise a process, which could  
    http://www.lukol.com/Top/Science/Math/Number_Theory/Diophantine_Equations/

72. Science/Math/Number Theory/Diophantine Equations
    the entire directory. Developing A General 2nd Degree diophantine equation x^2+ p = 2^n Methods to solve these equations.  
    http://www.ebroadcast-info.com/information/Science/Math/Number_Theory/Diophantin

73. Diophantine Equations
    factorization diophantine equations. One important use of algebraicnumbers is to answer questions about diophantine equations. We  
    http://mathcircle.berkeley.edu/BMC3/bamc/node3.html
    
    Extractions: Next: Read all about it! Up: bamc Previous: Unique and nonunique factorization One important use of algebraic numbers is to answer questions about Diophantine equations. We have already seen one example of this (representing an integer as the sum of two squares); let's consider a few more examples. The equation is (mis)named ``Pell's equation''. Over , we can factor the left side and rewrite the equation as This makes clear the multiplicative structure of the set of solutions: if and are solutions, then Moreover, we can sort all solutions into increasing order by (which is an increasing function of for , given that ). Now it's easy to see that all solutions in positive integers are ``powers'' of the smallest solution, assuming that any solutions exist. There are several ways to show that solutions exist. One method uses continued fractions and has been known at least for 1000 years (it occurs in an old Indian text); it is probably the best method for explicitly computing solutions. ASIDE: What does this have to do with algebraic numbers? What we've done is to classify the algebraic integers in the field whose products with their conjugates equal 1. An analogous classification can be made for an arbitrary number field, which solves the Pell equation along the way. What about the equation

74. Section 1.1 From "Hilbert's Tenth Problem" By Yuri MATIYASEVICH
    1.1 diophantine equations as a decision problem. Let us recall that a Diophantineequation is an equation of the form. D(x 1 , ,x m )=0,, (1.1.1).  
    http://logic.pdmi.ras.ru/~yumat/H10Pbook/par_1_1.htm
    
    Extractions: Section 1.1 from the book written by Yuri MATIYASEVICH 1.1 Diophantine equations as a decision problem Let us recall that a Diophantine equation is an equation of the form D x x m where D is a polynomial with integer coefficients. In addition to (1.1.1), Diophantine equations can be written in the more general form D L x x m D R x x m where D L and D R are again polynomials with integer coefficients. When we speak of ''an arbitrary Diophantine equation,'' we shall have in mind an equation of the form (1.1.1) since an equation of the form (1.1.2) can easily be transformed into an equation of the form (1.1.1) by transposing all the terms to the left-hand side. However, we will often use the notation (1.1.2) for particular equations if this form turns out to be easier to grasp. We shall also take another advantage of the more general form (1.1.2); namely, in this case we can demand that D L and D R are polynomials with non-negative coefficients. Diophantine equations typically have several unknowns, and we must distinguish the degree of with respect to a given unknown x i and the ( total degree of (1.1.1), i.e., the maximum, over all the monomials constituting the polynomial

75. Omniseek: Family: Search Results For 'diophantine Equations'
    (http//math.la.asu.edu/~jj/445/chapters/euclid/euclid.html) Hilbert s Tenth ProblemRate This Site Given a diophantine equation with any number of unknowns  
    http://family.omniseek.com/search/search.html?t=diophantine equations&mode=defau

76. SLCentral Directory - Science - Math - Number Theory - Diophantine Equations
    Developing A General 2nd Degree diophantine equation x^2 + p = 2^n Methods to solve these equations. » diophantine equations  
    http://www.slcentral.com/directory/index.php/Science/Math/Number_Theory/Diophant
    
    Extractions: Submit a Site SLCentral Directory - Science - Math - Number Theory - Diophantine Equations This category in other languages: Spanish - 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.

77. BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME DIOPHANTINE EQUATIONS
    BOUNDS FOR SMALL PRIME SOLUTIONS OF SOME diophantine equationS. Prof. MC Liu. Departmentof Mathematics HKU518/96P. 1. STORY OF THE PROBLEM AND OUR MAIN RESULTS.  
    http://www.hku.hk/rss/res_proj/54/54.htm
    
    Extractions: 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.

78. Diophantine Equations
    diophantine equations. JasperGifts.com. Shopping? diophantine equation diophantineequation linear. Links Science Math Number Theory diophantine equations.  
    http://www.jaspergifts.com/Science/Math/Number_Theory/Diophantine_Equations/

79. Section 2.3: Linear Diophantine Equations 1
    one goal of this chapter is to develop a systematic method for finding all integersolutions x and y (when there are any) to the linear diophantine equation.  
    http://www.mathlab.mtu.edu/COURSES/holt/dnt/euclid3.html
    
    Extractions: 2.3 Linear Diophantine Equations 1 As stated in the Prelab section, one goal of this chapter is to develop a systematic method for finding all integer solutions x and y (when there are any) to the linear diophantine equation a x b y c where a b , and c are integer constants. As you discovered when working on the Prelab exercises, for a given choice of a and b , equation (1) may have several solutions or possibly no solutions; it depends on the value of c . If we have specific values for a and b , how can we figure out the values of c for which equation (1) will have a solution? As a first step, let's look at the situation for a specific choice of a and b , say a = 6 and b = 4. In this case, the above equation becomes x y = c and our question is: For what values of c is there a solution to this equation? One way to approach this is to try plugging a bunch of different values for x and y into the left-hand side of (2), and see what we get out. After all, any value that comes out must be a suitable value for

80. Solving A System Of Linear Diophantine Equations With Lower And
    And .. Aardal, Hurkens, Lenstra (1998) (Correct) 14.8% An Algorithmfor Solving a diophantine equation With.. - Aardal, Lenstra  
    http://citeseer.ist.psu.edu/329160.html

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