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Diophantine Equation: more books (88)

Solutions of the Diophantine equation X² = DY=K, by Mohan Lal, 1968
Diophantine Equations by L. J. Mordell, 1970
Diophantine equations: Lectures given by W.J. Ellison, 1971-1972 by William John Ellison, 1972
New methods for solving quadratic diophantine equations (part I and part II) (Research report) by A. G Schaake, 1989
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
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
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
Diophantine equations in division algebras, by Ralph G Archibald, 1927
On pairs of diophantine equations by Amin Abdul K Muwafi, 1959
Notes on the Diophantine equation yÂ²-k=xÂ³ (Arkiv foÌˆr matematik) by Ove Hemer, 1954
Analytic methods for Diophantine equations and Diophantine inequalities;: [lecture notes] the University of Michigan, fall semester, 1962 by Harold Davenport, 1962
On the diophantine equation: Ap[x]+bq[y]=c+dp[z]q[w] by Christopher Skinner, 1989
The development and appraisal of a unit on Diophantine equations for prospective elementary school teachers by Tommy Harold Richard, 1971
On the Diophantine equation 1[superscript k] - 2[superscript k] -...- x[superscript k] - R(x) = y[superscript z] (Afdeling zuivere wickunde ; ZW 113/78) by Marc Voorhoeve, 1978

lists with details

Diophantine Equation--Linear
diophantine equation encyclopedia article about Diophantine encyclopedia article about diophantine equation. diophantine equation in Freeonline English dictionary, thesaurus and encyclopedia. diophantine equation.
http://hades.ph.tn.tudelft.nl/Internal/PHServices/Documentation/MathWorld/math/m
Diophantine Equations
diophantine equations. A diophantine equation is one in which thesolutions must be integers or rational numbers. On this page we
http://www25.brinkster.com/ranmath/diophan/

Extractions: var google_language="en"; var adHB=true; wDoL("top","RR1WOKH"); wCls("RR1WOKH"); wDoL("btm","RR1WOKH"); showA("RR1WOKH"); A Diophantine equation is one in which the solutions must be integers or rational numbers. On this page we shall restrict ourselves to solutions in positive integers. Let us imagine one's experience on his first encounter with the following puzzle: There's Dad and Ma and Brother and Me; And she is three times Me. How old is Dad? The ordinary algebra student says, "Hey, I can't solve these equations because there are four unknowns and only three equations." Indeed there is no unique solution over the field of the real numbers, but there is a unique solution in integers. Here is another problem of the same sort: At Jimmy's school four-fifths of the students use five-sixths of the desks. What is the smallest possible number of students in the class? Take these problems to school, bring them up in math class, and watch Teacher slowly turn into a babbling idiot. Before turning to the formal theory of Diophantine equations, let us see what a little common sense will do.
Diophantine Equations
Thus we have a simple general method allowing to determine, given an arbitrarylinear diophantine equation with two unknowns, has it solutions in integer
http://www25.brinkster.com/ranmath/diophan/diophan.htm

Extractions: var google_language="en"; var adHB=true; wDoL("top","QQ0VNJG"); wCls("QQ0VNJG"); wDoL("btm","QQ0VNJG"); showA("QQ0VNJG"); The following material is mostly quoted from a web page created by Dr. Karlis Podnieks of the University of Latvia. The original is (or was) here Linear Diophantine equations Problems that can be solved by finding solutions of algebraic equations in the domain of integer numbers have been known since the very beginning of mathematics. Some of these equations do not have solutions at all. For example, the equation 2x-2y=1 cannot have solutions in the domain of integer numbers since its left-hand side is always an even number. Some other equations have a finite set of solutions. For example, the equation 3x=6 has only one solution x=2. And finally, some equations have an infinite set of integer solutions. For example, let us solve the equation 7x-17y=1: x = (17y+1)/7 = 2y + (3y+1)/7. The number (3y+1)/7 must be integer, let us denote it by z.Then 3y+1=7z and x=2y+z. Thus we have arrived at the equation3y-7z=-1 having smaller coefficients than the initial one. Let us apply our "coefficient reduction method" once more: y = (7z-1)/3 = 2z + (z-1)/3.
Linear Diophantine Equations
Previous The greatest common divisor Contents Index Linear diophantineequations. Diophantus, a Greek mathematician who lived during
http://web.usna.navy.mil/~wdj/book/node7.html

Extractions: Next: Binary and -ary notation Up: Divisibility Previous: The greatest common divisor Contents Index Diophantus, a Greek mathematician who lived during the 4th century A.D., was one of the first people who attempted to find integral or rational solutions to a given system of equations. Often the system involves more unknowns than equations. We will consider a linear equation, , with two unknowns Theorem 1.2.17 The linear equation has no solutions if does not divide . If does divide then there are infinitely many solutions given by: where is any solution and is any integer. proof : The first part of the theorem follows from lemma . Let be any solution, and let be any other solution. We want to show that and , where . Substitute into the equation: Therefore, . If we can divide both sides of this equation by Since (see the Exercise ), it follows that . Substituting into the above equation gives: and our proof is complete. Corollary 1.2.18 If then proof : Assume . Let . By the above theorem, there exist integers
Randomness In Arithmetic
The mathematical assertion that the diophantine equation with parameter k has nosolution encodes the assertion that the kth computer program never halts.
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer2.html

Extractions: It is impossible to prove whether each member of a family of algebraic equations has a finite or an infinite number of solutions: the answers vary randomly and therefore elude mathematical reasoning. What could be more certain than the fact that 2 plus 2 equals 4? Since the time of the ancient Greeks mathematicians have believed there is little-if anything-as unequivocal as a proved theorem. In fact, mathematical statements that can be proved true have often been regarded as a more solid foundation for a system of thought than any maxim about morals or even physical objects. The 17th-century German mathematician and philosopher Gottfried Wilhelm Leibniz even envisioned a ``calculus'' of reasoning such that all disputes could one day be settled with the words ``Gentlemen, let us compute!'' By the beginning of this century symbolic logic had progressed to such an extent that the German mathematician David Hilbert declared that all mathematical questions are in principle decidable, and he confidently set out to codify once and for all the methods of mathematical reasoning. This result, which is part of a body of work called algorithmic information theory, is not a cause for pessimism; it does not portend anarchy or lawlessness in mathematics. (Indeed, most mathematicians continue working on problems as before.) What it means is that mathematical laws of a different kind might have to apply in certain situations: statistical laws. In the same way that it is impossible to predict the exact moment at which an individual atom undergoes radioactive decay, mathematics is sometimes powerless to answer particular questions. Nevertheless, physicists can still make reliable predictions about averages over large ensembles of atoms. Mathematicians may in some cases be limited to a similar approach.
Science Search > Diophantine Equations
6.00 Votes 555. 3. Developing A General 2nd Degree diophantine equationx^2 + p = 2^n Methods to solve these equations. http//www
http://www.science-search.org/index/Math/Number_Theory/Diophantine_Equations/
Hilbert's Tenth Problem. Diophantine Equations. Part 2. By K.Podnieks
4.4. Diophantine Representation of Solutions of Fermat s Equation. Jones, JP Universaldiophantine equation. Journal of Symbolic Logic, 47 (1982), 549571.
http://www.ltn.lv/~podnieks/gt4a.html

Extractions: Back to title page Left Adjust your browser window Right We will investigate only a special (the simplest!) case of Fermat's equation - where D=a x - (a -1)y No problems to prove the existence of non-trivial solutions for this equation: you can simply take x=a, y=1. After this, all the other natural solutions we can calculate by using the following smart idea. Let us note that x - (a -1)y = (x+y*sqrt(a -1)) * (x-y*sqrt(a Take our first non-trivial solution x=a, y=1: a - (a -1) = (a+sqrt(a -1)) * (a-sqrt(a Consider the n-th power: (a+sqrt(a n * (a-sqrt(a n Now let us apply the Newton's binomial formula to the expression (a+sqrt(a n . For example, if n=2, then (a+sqrt(a = a + 2a*sqrt(a -1) + (a I.e. some of the items contain sqrt(a -1), and some do not. Let us sum up either kind of the items: (a+sqrt(a n = x n (a) + y n (a)sqrt(a where x n (a), y n (a) are natural numbers. For example, x (a)=2a -1, y
Detalji ZProjekta
Keywords Explicit solutions of diophantine equations, Diophantine mtuples, ellipticcurves of high rank, Thue equation, systems of simultaneous Pellian
http://www.mzos.hr/zProjekti/result_det.asp?ID=0037110
Diophantine Equation -- From MathWorld
Number Theory diophantine equations A diophantine equation is an algebraic equation in one or more unknownswith integer coefficients, for which integer solutions are sought.
http://www.astro.virginia.edu/~eww6n/math/DiophantineEquation.html

Extractions: Diophantine Equation A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution. Such an algorithm does exist for the solution of first-order Diophantine equations. However, the impossibility of obtaining a general solution was proven by Yuri Matiyasevich in 1970 (Matiyasevich 1970, Davis 1973, Davis and Hersh 1973, Davis 1982, Matiyasevich 1993) by showing that the relation (where is the th Fibonacci number ) is Diophantine. 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
3. Diophantine Equations And Logic
3. diophantine equations and logic. I believe logical statements. A statementcan be seen as a ``diophantine equation where we have.
http://www.hf.uio.no/filosofi/njpl/vol1no2/pioneer/node3.html

Extractions: Next: 4. Introducing new symbols Up: Thoralf Skolem: Pioneer of Previous: 2. Vita I believe that Skolem considered Diophantine equations and logic as one subject. Let me indicate a little speculatively how Skolem's thought might have been. The theory of Diophantine equations considers questions about satisfiability of equations like
Diophantine Equations Information Sites
Top Science Math Number Theory diophantine equations Developing A General 2ndDegree diophantine equation x^2 + p = 2^n Methods to solve these equations.
http://numbersorg.com/NumberTheory/DiophantineEquations/

Extractions: Equal Sums of Like Powers Fermat's Last Theorem Linear Diophantine Equations - A web tool for solving Diophantine equations of the form ax + by = c. Bibliography on Hilbert's Tenth Problem - Searchable, ~400 items. Diophantine Equations - Dave Rusin's guide to Diophantine equations. Egyptian Fractions - Lots of information about Egyptian fractions collected by David Eppstein. The Erdos-Strauss Conjecture Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Methods to solve these equations. Thue Equations - Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger. Hilbert's Tenth Problem - Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites. Diophantine Geometry in Characteristic p - A survey by Jos© Felipe Voloch. Pythagorean Triplets - A Javascript calculator for pythagorean triplets.
Linear Diophantine Equations
Generally this functions is used in connection with operations on latticesbecause a lattice can be seen as a solution of a diophantine equation.
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.
Open Problem? Diophantine Equations.
Open problem given a diophantine equation that has a solution for every n eg a+b+c =abc ,compute the expected number of steps until a solution is found.
http://semillon.wpi.edu/~aofa/AofA/msg00031.html

Extractions: ANALYSIS of ALGORITHMS Bulletin Board Date Prev Date Next Thread Prev Thread Next ... Thread Index http://www.geocities.com/markoriedelde/index.html http://www.geocities.com/markoriedelde/index.html Follow-Ups Open problem? Diophantine equations. , Marko Riedel, 03/12/2004 References A challenge for hispanophones. , Marko Riedel, 02/11/2004 Prev by Date: A challenge for hispanophones. Next by Date: Re: Una verdadera maravilla. (Sister Celine.) Previous by thread: A challenge for hispanophones. Next by thread: Open problem? Diophantine equations. Index(es): Date Thread
Open Problem? Diophantine Equations.
Open problem? diophantine equations. diophantine equations. From Marko Riedel mriedel@xxxxxxxxxxxxx ; Date Fri, 12 Mar 2004 145955 +0100.
http://semillon.wpi.edu/~aofa/AofA/msg00033.html

Extractions: ANALYSIS of ALGORITHMS Bulletin Board Date Prev Date Next Thread Prev Thread Next ... Thread Index Hi folks, I spent a week learning how to manipulate hypercomplex numbers in order to compute certain combinatorial sums and wrote a Maple library for this purpose. It's on my combinatorics page on my home page. http://www.geocities.com/markoriedelde/combnumth.html http://www.geocities.com/markoriedelde/index.html References A challenge for hispanophones. , Marko Riedel, 02/11/2004 Open problem? Diophantine equations. , Marko Riedel, 02/27/2004 Prev by Date: Re: Una verdadera maravilla. (Sister Celine.) Next by Date: Hypercomplex numbers and combinatorial sums. (II) Previous by thread: Open problem? Diophantine equations. Next by thread: Hypercomplex numbers and combinatorial sums. (II) Index(es): Date Thread
Diophantine Equations Number Theory Math Science
Developing A General 2nd Degree diophantine equation x^2 + p = 2^n www.biochem.okstate.edu/OAS/OJAS/thiendo.htmMath Number Theory diophantine equations.
http://www.interactiva.org/Dir/I/English/Science/Math/Number_Theory/Diophantine_

Extractions: www.interactiva.org English Deutsch Espa±ol ... Diophantine Equations Diophantine Equations : In this seccionre included any equation or set of equations where the unknowns must be integer numbers. It includes Fermat Last Theorem as a special case. Math Number Theory Diophantine Equations: Equal Sums of Like Powers
Diophantine Equation
Diophantine linear equation. ALGORITHM. My Diophant algorithm solves almostalways diophantine equation for N =500 and AI =2*10**9. IMPLEMENTATION.
http://www.geocities.com/SiliconValley/Garage/3323/aat/a_diop.html
Diophantine Equation Definition Meaning Information Explanation
diophantine equation definition, meaning and explanation and moreabout diophantine equation. Free diophantine equation. definition
http://www.free-definition.com/Diophantine-equation.html

Extractions: Google News about your search term In mathematics Diophantine equations are equation s 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. A traditional name for the study of Diophantine equations is Diophantine analysis . The questions asked include: Such problems often lay unsolved for centuries, and mathematicians gradually came to understand their depth (in some cases), rather than treat them as puzzles. Mathematical logic now has shown that it is hopeless to expect a complete theory. The point of view of Diophantine geometry , which is the application of algebraic geometry techniques in this field, has continued to grow as a result; since treating
Diophantine Equation :: Online Encyclopedia :: Information Genius
diophantine equation. Online Encyclopedia Diophantine values. Examplesof diophantine equations are ax + by = 1 See Bézout s identity.
http://www.informationgenius.com/encyclopedia/d/di/diophantine_equation.html

Extractions: 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. This content from wikipedia is licensed under the GNU Free Documentation License Power Supplies Hardware Information Law Advice
Diophantine Equation From FOLDOC
diophantine equation. mathematics Equations with integer coefficientsto which integer solutions are sought. Because the results
http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Diophantine equation
DIOPHANTINE EQUATION - Meaning And Definition Of The Word
diophantine equation Dictionary Entry and Meaning. Computing Dictionary. DefinitionEquations with integer coefficients to which integer solutions are sought.
http://www.hyperdictionary.com/computing/diophantine equation

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