Download or read book The Algorithmic Resolution of Diophantine Equations written by Nigel P. Smart and published by Cambridge University Press. This book was released on 1998-11-12 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent account of the computational methods used to solve diophantine equations.
Download or read book The Algorithmic Resolution of Diophantine Equations written by Nigel P. Smart and published by . This book was released on 1998 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent account of the computational methods used to solve diophantine equations.
Download or read book The Algorithmic Resolution of Diophantine Equations written by Nigel Paul Smart and published by . This book was released on 2014-05-14 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent account of the computational methods used to solve diophantine equations.
Download or read book Algorithms for Diophantine Equations written by Benne M. M. De Weger and published by . This book was released on 1989 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Diophantine Equations and Power Integral Bases written by István Gaál and published by Springer Nature. This book was released on 2019-09-03 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
Download or read book Diophantine Equations and Power Integral Bases written by Istvan Gaal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
Download or read book Solving Diophantine Equations written by Octavian Cira and published by Infinite Study. This book was released on 2014 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation η(π(x)) = π(η(x)), where η is the Smarandache function and π is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and then we check all possible situations, and of course we retain among them only those solutions that verify our equation. In other words, we say that the equation does not have solutions in the search domain, or the equation has n solutions in this domain. This mode of solving is called partial resolution. Partially solving a Diophantine equation may be a good start for a complete solving of the problem. The authors have identified 62 Diophantine equations that impose such approach and they partially solved them. For an efficient resolution it was necessarily that they have constructed many useful ”tools” for partially solving the Diophantine equations into a reasonable time. The computer programs as tools were written in Mathcad, because this is a good mathematical software where many mathematical functions are implemented. Transposing the programs into another computer language is facile, and such algorithms can be turned to account on other calculation systems with various processors.
Download or read book Diophantine Analysis written by Jorn Steuding and published by CRC Press. This book was released on 2005-05-19 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers. Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.
Download or read book Discriminant Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2017 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.
Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, graduate-level treatment of unit equations and their various applications.
Download or read book Quadratic Diophantine Equations written by Titu Andreescu and published by Springer. This book was released on 2015-06-29 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell’s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.
Download or read book The Algorithmic Solution of Diophantine Equations written by Mahadi Ddamulira and published by . This book was released on 2016-12-10 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Diophantus and Diophantine Equations written by Isabella Grigoryevna Bashmakova and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus—a person whose very existence has long been doubted by most historians of mathematics—will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman, who notes the most recent developments including the proof of Fermat's Last Theorem.
Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.
Download or read book Diophantine Equations and the Cubic Ambiguity Resolution Algorithm written by and published by . This book was released on 1982 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ambiguity resolution problem for the TOAME four phase interferometer system is presented in terms of the integer solutions of systems of linear equations. (Author).
Download or read book Algorithms for the Solution of Systems of Linear Diophantine Equations written by Joseph Tsu-wu Chou and published by . This book was released on 1979 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Diophantine Equations written by and published by Academic Press. This book was released on 1969 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine Equations
