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Author : Hideo Yokoi
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (165 download)
Download or read book Solvability of the diophantine equation x 2 - Dy 2 written by Hideo Yokoi and published by . This book was released on 1993 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Titu Andreescu
Publisher : Springer
ISBN 13 : 0387541098
Total Pages : 224 pages
Book Rating : 4.3/5 (875 download)
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.
Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 0817645497
Total Pages : 350 pages
Book Rating : 4.8/5 (176 download)
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.
Author : Bogdan Grechuk
Publisher : Springer Nature
ISBN 13 : 3031629493
Total Pages : 824 pages
Book Rating : 4.0/5 (316 download)
Download or read book Polynomial Diophantine Equations written by Bogdan Grechuk and published by Springer Nature. This book was released on with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. A. Mollin
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (897 download)
Download or read book All Solutions of the Diophantine Equation $ X^2 - Dy^ 2 + N* $ written by R. A. Mollin and published by . This book was released on 1998 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Umberto Zannier
Publisher : Springer
ISBN 13 : 8876425179
Total Pages : 248 pages
Book Rating : 4.8/5 (764 download)
Download or read book Lecture Notes on Diophantine Analysis written by Umberto Zannier and published by Springer. This book was released on 2015-05-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.
Author : Thomas Koshy
Publisher : Springer
ISBN 13 : 1461484898
Total Pages : 444 pages
Book Rating : 4.4/5 (614 download)
Download or read book Pell and Pell–Lucas Numbers with Applications written by Thomas Koshy and published by Springer. This book was released on 2014-11-11 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences. A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book. Finally, Pell and Pell–Lucas Numbers provides enjoyment and excitement while sharpening the reader’s mathematical skills involving pattern recognition, proof-and-problem-solving techniques.
Author : Trygve Nagell
Publisher : American Mathematical Soc.
ISBN 13 : 1470463245
Total Pages : 309 pages
Book Rating : 4.4/5 (74 download)
Download or read book Introduction to Number Theory written by Trygve Nagell and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: A special feature of Nagell's well-known text is the rather extensive treatment of Diophantine equations of second and higher degree. A large number of non-routine problems are given. Reviews & Endorsements This is a very readable introduction to number theory, with particular emphasis on diophantine equations, and requires only a school knowledge of mathematics. The exposition is admirably clear. More advanced or recent work is cited as background, where relevant … [T]here are welcome novelties: Gauss's own evaluation of Gauss's sums, which is still perhaps the most elegant, is reproduced apparently for the first time. There are 180 examples, many of considerable interest, some of these being little known. -- Mathematical Reviews
Author : L. Pacholski
Publisher : Springer
ISBN 13 : 354038393X
Total Pages : 420 pages
Book Rating : 4.5/5 (43 download)
Download or read book Model Theory of Algebra and Arithmetic written by L. Pacholski and published by Springer. This book was released on 2006-11-15 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : FLORENTIN SMARANDACHE
Publisher : Infinite Study
ISBN 13 :
Total Pages : 7 pages
Book Rating : 4./5 ( download)
Download or read book A Method to Solve the Diophantine Equation written by FLORENTIN SMARANDACHE and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here, we show that: if the equation has an integer solution and a⋅b is not a perfect square, then (1) has an infinitude of integer solutions; in this case we find a closed expression for (xn,yn), the general positive integer solution, by an original method. More, we generalize it for any Diophantine equation of second degree and with two unknowns.
Author : Craig Smorynski
Publisher : Springer Science & Business Media
ISBN 13 : 3642754627
Total Pages : 416 pages
Book Rating : 4.6/5 (427 download)
Download or read book Logical Number Theory I written by Craig Smorynski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory as studied by the logician is the subject matter of the book. This first volume can stand on its own as a somewhat unorthodox introduction to mathematical logic for undergraduates, dealing with the usual introductory material: recursion theory, first-order logic, completeness, incompleteness, and undecidability. In addition, its second chapter contains the most complete logical discussion of Diophantine Decision Problems available anywhere, taking the reader right up to the frontiers of research (yet remaining accessible to the undergraduate). The first and third chapters also offer greater depth and breadth in logico-arithmetical matters than can be found in existing logic texts. Each chapter contains numerous exercises, historical and other comments aimed at developing the student's perspective on the subject, and a partially annotated bibliography.
Author : Michael Jacobson
Publisher : Springer Science & Business Media
ISBN 13 : 038784922X
Total Pages : 504 pages
Book Rating : 4.3/5 (878 download)
Download or read book Solving the Pell Equation written by Michael Jacobson and published by Springer Science & Business Media. This book was released on 2008-12-02 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pell’s Equation is a very simple Diophantine equation that has been known to mathematicians for over 2000 years. Even today research involving this equation continues to be very active, as can be seen by the publication of at least 150 articles related to this equation over the past decade. However, very few modern books have been published on Pell’s Equation, and this will be the first to give a historical development of the equation, as well as to develop the necessary tools for solving the equation. The authors provide a friendly introduction for advanced undergraduates to the delights of algebraic number theory via Pell’s Equation. The only prerequisites are a basic knowledge of elementary number theory and abstract algebra. There are also numerous references and notes for those who wish to follow up on various topics.
Author : Edward Everett Whitford
Publisher :
ISBN 13 :
Total Pages : 199 pages
Book Rating : 4.L/5 ( download)
Download or read book The Pell Equation written by Edward Everett Whitford and published by . This book was released on 1912 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Don Redmond
Publisher : CRC Press
ISBN 13 : 1000148572
Total Pages : 778 pages
Book Rating : 4.0/5 (1 download)
Download or read book Number Theory written by Don Redmond and published by CRC Press. This book was released on 2020-09-29 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.
Author : G. O. Jones
Publisher : Cambridge University Press
ISBN 13 : 1107462495
Total Pages : 235 pages
Book Rating : 4.1/5 (74 download)
Download or read book O-Minimality and Diophantine Geometry written by G. O. Jones and published by Cambridge University Press. This book was released on 2015-08-13 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings the researcher up to date with recent applications of mathematical logic to number theory.
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Author : David Tutherly Walker
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.3/5 (21 download)
Download or read book On the Diophantine Equation A[superscript]x - B[superscript]y written by David Tutherly Walker and published by . This book was released on 1955 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard A. Mollin
Publisher : CRC Press
ISBN 13 : 1351420763
Total Pages : 422 pages
Book Rating : 4.3/5 (514 download)
Download or read book Quadratics written by Richard A. Mollin and published by CRC Press. This book was released on 2018-04-27 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows the browser to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders. This is not a book that is primarily about tables, although there are 80 pages of appendices that contain extensive tabular material (class numbers of real and complex quadratic fields up to 104; class group structures; fundamental units of real quadratic fields; and more!). This book is primarily a reference book and graduate student text with more than 200 exercises and a great deal of hints! The motivation for the text is best given by a quote from the Preface of Quadratics: "There can be no stronger motivation in mathematical inquiry than the search for truth and beauty. It is this author's long-standing conviction that number theory has the best of both of these worlds. In particular, algebraic and computational number theory have reached a stage where the current state of affairs richly deserves a proper elucidation. It is this author's goal to attempt to shine the best possible light on the subject."
