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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. AoPS Math Forum :: View Topic - Diophantine Equation
    The time now is Fri Aug 05, 2005 806 am All times are GMT 7 Hours, Diophantineequation, Mark the topic unread Math Forum » Olympiad Section » Number  
    http://www.artofproblemsolving.com/Forum/topic-46449.html
    
    Extractions: Posted: Mon Aug 01, 2005 12:20 am Post subject: Diophantine equation The problem is actually from the Russian Math Olympiad this year. Using very advanced number theory, I managed to prove that the following equations do not have integer solutions. Unfortunately, I would truly appreciate an elegant or elementary solution to the problem:

62. AoPS Math Forum :: View Topic - Easy Diophantine Equation
    All times are GMT 7 Hours, Easy diophantine equation 2005 659 pm Postsubject Easy diophantine equation, 1 Mark this post and the followings unread  
    http://www.artofproblemsolving.com/Forum/topic-46028.html

63. Applicatons - Solve Diophantine Equations
    Instructions This function will enable one to find all integer solutions to theabove 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

64. Continued Fractions - Introduction
    Equations of the first form are called diophantine equations. Those of the secondform are named Pell s equations. Definition 10  
    http://archives.math.utk.edu/articles/atuyl/confrac/intro.html
    
    Extractions: To introduce this web site, the most appropriate place to start is with a definition of a continued fraction. A continued fraction refers to all expressions of the form where a ,a ,a ,.... and b ,b ,b ,... are either real or complex values. The number of terms can be either finite or infinite. Let me answer this question by first explaining what you will not find at this site. You will not find any deep analysis of continued fractions. For those of you researching this area, I direct your attention to the resources Even though this site does not go into great analysis of continued fractions, it does cover some of the basic theorems of the field. For those of you who are "math-phobic," now would probably be a good time to leave. When I created this site, my intention was to provide a brief introduction to this fascinating area of mathematics. I have aimed this presentation at those at my own level, that is, those at an undergraduate level with an interest in mathematics. For many, this may be a first introduction to continued fractions since this subject, if it is taught at all, is restricted to a single chapter in a number theory text. Hopefully this site will inspire others to study continued fractions in greater detail. I have broken this site into four main pieces. In the first section, which is found below, I present some of the basic theorems about simple continued fractions. In the second

65. Mathematical Programming Glossary Page 2
    diophantine equations. A system of equations whose variables must be In general, solving the linear diophantine equations, Ax=b for x in Zn,  
    http://carbon.cudenver.edu/~hgreenbe/glossary/second.php?page=D.html

66. Science: Mathematics: Number Theory: Diophantine Equations - Open Site
    Science Mathematics Number Theory diophantine equations Open Site.  
    http://open-site.org/Science/Mathematics/Number_Theory/Diophantine_Equations/

67. Diophantine Equation From FOLDOC
    diophantine equation. mathematics Equations with integer coefficients to whichinteger solutions are sought. Because the results are restricted to  
    http://foldoc.doc.ic.ac.uk/foldoc/foldoc.cgi?Diophantine equation

68. MATLAB Central File Exchange - Generate Many Examples Of Ramanujam's Diophantine
    x y and u v and N that satisfy the diophantine equation x^3 + y^3 = u^3 +v^3 = N where the four integers x, y, u, v have no common factor.  
    http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=5870&ob

69. Gcd (MATLAB Functions)
    These are useful for solving diophantine equations and computing In the nextexample, we solve for x and y in the diophantine equation 30x + 56y = 8 .  
    http://www.mathworks.com/access/helpdesk/help/techdoc/ref/gcd.html
    
    Extractions: G = gcd(A,B) returns an array containing the greatest common divisors of the corresponding elements of integer arrays A and B . By convention, gcd(0,0) returns a value of ; all other inputs return positive integers for G [G,C,D] = gcd(A,B) returns both the greatest common divisor array G , and the arrays C and D , which satisfy the equation: A(i).*C(i) + B(i).*D(i) = G(i) . These are useful for solving Diophantine equations and computing elementary Hermite transformations. Examples

70. Diophantine Equations In Naturals -- References
    Solving linear diophantine equations using the geometric structure of the the 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. Linear Diophantine Equations
    Linear diophantine equations are linear equations in which only integer solutionsare allowed. Consider a system of $m$ equations in $n$ variables for which  
    http://www.irisa.fr/polylib/DOC/node33.html
    
    Extractions: To solve such a sytems, first the rows of are rearranged in such a way that the first rows of are the ones which contribute to the rank. This is done with: Then the function SolveDiophantine for solving the equation can be used. If a solution exists, the procedure returns , otherwise it returns Generally this functions is used in connection with operations on lattices because a lattice can be seen as a solution of a Diophantine equation.

72. Diophantine Equation
    diophantine equation by Annie (Nov 30, 2004). Re diophantine equation by mars (Dec1, 2004) Re Re diophantine equation by mars (Dec 2, 2004)  
    http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2004;task=show_msg;msg=0

73. AMCA: On The Diophantine Equation $p^x-q^y=c$ By Florian Luca
    The diophantine equation pxqy=c in positive integers (p, q, x, y, c) with p andq distinct primes has received considerable interest.  
    http://at.yorku.ca/c/a/k/l/14.htm
    
    Extractions: UNAM The diophantine equation p x -q y =c in positive integers (p, q, x, y, c) with p and q distinct primes has received considerable interest. What is usually of interest for this equation is the following question: Given p and q, find all the values of c for which the above equation has at least two distinct solutions (x, y). The existence of two solutions (x, y) for the above equation reduces to the existence of a nontrivial solution of the equation p x -q y =p x -q y in positive integers (x , y , x , y ), where by nontrivial we mean that (x , y ) =/= (x , y In my talk, I will present two results concerning equation (1). I will first show that if one of the primes p and q, say p, is fixed, then there exist only finitely many quintuples of positive integers (q, x , y , x , y ) with q =/= p and prime which give a nontrivial solution of (1). I will then show that the ABC-conjecture implies that there should exist only finitely many sixtuples of positive integers (p, q, x

74. Section 2.3: Linear Diophantine Equations 1
    2.3 Linear diophantine equations 1. As stated in the Prelab section, one goal ofthis chapter is to develop a systematic method for finding all integer  
    http://www.math.mtu.edu/mathlab/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

75. Section 2.5: Linear Diophantine Equations 2
    2.5 Linear diophantine equations 2. Now we re getting somewhere. With the researchquestions in the preceding section complete, we now know all of the  
    http://www.math.mtu.edu/mathlab/COURSES/holt/dnt/euclid5.html
    
    Extractions: 2.5 Linear Diophantine Equations 2 Now we're getting somewhere. With the research questions in the preceding section complete, we now know all of the solutions to the equation a x b y d where d = gcd( a b ). Therefore, it remains to determine all of the solutions to the equation a x b y c where c kd and k is an integer. To get a feel for what is going on, let's look at an example. In the preceding section, we looked at the equation 7 x y = 1. Let's change this a bit, say to x y Using the Euclidean Algorithm, we found that x y x y = 1. Thus, it is easy to see that x y x y = 5. What about the other solutions? The applet from the previous section can be used to search for additional solutions: Your browser does not support java. Suppose that gcd( a b d and that ( x y ) is a solution to a x b y d . Find the general form of all solutions ( x y ) to a x b y k d giving x in terms of x and y in terms of y Section 2.1 Section 2.2 Section 2.3 Section 2.4 ... DNT Table of Contents

76. LMS JCM (8) 116-121
    Motivated by this point of view, an example of a diophantine equation The diophantine equation has four terms rather than the usual three terms  
    http://www.lms.ac.uk/jcm/8/lms2004-056/
    
    Extractions: Abstract: Several classes of Fermat-type diophantine equations have been successfully resolved using the method of galois representations and modularity. In each case, it is possible to view the proper solutions to the diophantine equation in question as corresponding to suitably defined integral points on a modular curve of level divisible by 2 or 3. Motivated by this point of view, an example of a diophantine equation associated to the modular curve X0(5) is discussed in this paper. The diophantine equation has four terms rather than the usual three terms characteristic of generalized Fermat equations. This paper is available as (94 KB)

77. Science Math Number Theory Diophantine Equations - Science Math Number Theory Di
    Science Math Number Theory diophantine equations , web directory and searchengine, featuring a directory of millions of links along with thumbnails of  
    http://www.abc.net/directory/Science/Math/Number_Theory/Diophantine_Equations/

78. The Diophantine Equation P(x) = N! And A Result Of M. Overholt
    2000 Mathematics Subject Classification. 11D85. Key words and phrases. ABCConjecture,diophantine equations. Glasnik Matematicki Home Page.  
    http://www.math.hr/glasnik/vol_37/no2_04.html
    
    Extractions: e-mail: fluca@matmor.unam.mx Abstract. In this note, we show that the ABC-conjecture implies that a diophantine equation of the form P x n ! with P a polynomial with integer coefficients and degree d > 1 has only finitely many integer solutions ( x n ) with n 2000 Mathematics Subject Classification. Key words and phrases. ABC-Conjecture, diophantine equations. Glasnik Matematicki Home Page

79. Solving The Diophantine Equation Ax^2+by^2=m By Cornacchia's Method
    Solving the diophantine equation ax2+by2=m by Cornacchia s method. Here a 0,b 0,m a+b, gcd(a,m)=1=gcd(a,b). The algorithm is from A. Nitaj,  
    http://www.numbertheory.org/php/cornacchia.html

80. Gödel's Theorem
    For example, 11x538xy8+18133=0 is a diophantine equation. Solving Diophantineequations - ie finding their solutions or showing that they have no  
    http://www.sm.luth.se/~torkel/eget/godel/self.html
    
    Extractions: The original proof of Gödel's theorem uses the so-called Gödel sentence G for a theory T. This sentence is usually described as a sentence which says of itself that it is unprovable in T, or as a formalization of "I am unprovable in T" or "this sentence is unprovable in T". The Gödel sentence is in fact self-referential in the specific sense that it has the form A(t), where it is provable in a weak arithmetical theory that the value of the term t is the Gödel number of the formula A(t) itself. As a consequence, a certain equivalence is a theorem of T. This equivalence has the form "G holds if and only if the formula satisfying ... is not a theorem of T", where the formula satisfying ... is in fact the formula G itself. This equivalence is what is used in Gödel's proof of the incompleteness theorem. Thus it makes good sense to say that the Gödel sentence G is self-referential, and there is no mystery about how sentences that are in this sense self-referential can be constructed (in various ways) for different theories T. Gödel's original proof of his theorem, using the Gödel sentence G, is vivid and memorable, but it has given many people the incorrect impression that G must be used to prove the incompleteness theorem for T, or that sentences undecidable in T must be in this sense self-referential.

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