An Introduction To Diophantine Equations

Author : Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 40,8 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9780817645496

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An Introduction to Diophantine Equations by Titu Andreescu,Dorin Andrica,Ion Cucurezeanu Pdf

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 : Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
Publisher : Birkhäuser
Page : 345 pages
File Size : 54,9 Mb
Release : 2011-03-02
Category : Mathematics
ISBN : 0817672036

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An Introduction to Diophantine Equations by Titu Andreescu,Dorin Andrica,Ion Cucurezeanu Pdf

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 : Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
Publisher : Birkhäuser
Page : 345 pages
File Size : 43,9 Mb
Release : 2010-09-13
Category : Mathematics
ISBN : 0817645489

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An Introduction to Diophantine Equations by Titu Andreescu,Dorin Andrica,Ion Cucurezeanu Pdf

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 : Titu Andreescu,Dorin Andrica
Publisher : Unknown
Page : 198 pages
File Size : 52,7 Mb
Release : 2002
Category : Diophantine equations
ISBN : 9739238882

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An Introduction to Diophantine Equations by Titu Andreescu,Dorin Andrica Pdf

Author : Daniel Duverney
Publisher : World Scientific
Page : 348 pages
File Size : 49,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814307468

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Number Theory by Daniel Duverney Pdf

This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory. Clear, concise, and self-contained, the topics are covered in 12 chapters with more than 200 solved exercises. The textbook may be used by undergraduates and graduate students, as well as high school mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, the fascinating branch of mathematics.

Author : Istvan Gaal
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200857

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Diophantine Equations and Power Integral Bases by Istvan Gaal Pdf

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.

Author : Isabella Grigoryevna Bashmakova
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 47,7 Mb
Release : 2019-01-29
Category : Mathematics
ISBN : 9781470450496

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Diophantus and Diophantine Equations by Isabella Grigoryevna Bashmakova Pdf

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.

Author : H. Davenport
Publisher : Cambridge University Press
Page : 160 pages
File Size : 42,9 Mb
Release : 2005-02-07
Category : Mathematics
ISBN : 0521605830

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Analytic Methods for Diophantine Equations and Diophantine Inequalities by H. Davenport Pdf

Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.

Author : Anonim
Publisher : Academic Press
Page : 311 pages
File Size : 52,9 Mb
Release : 1969
Category : Mathematics
ISBN : 0080873421

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Diophantine Equations by Anonim Pdf

Diophantine Equations

Author : Titu Andreescu,Dorin Andrica
Publisher : Springer
Page : 211 pages
File Size : 55,6 Mb
Release : 2015-06-29
Category : Mathematics
ISBN : 9780387541099

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Quadratic Diophantine Equations by Titu Andreescu,Dorin Andrica Pdf

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 : Pietro Corvaja
Publisher : Springer
Page : 75 pages
File Size : 53,6 Mb
Release : 2016-11-23
Category : Mathematics
ISBN : 9789811026485

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Integral Points on Algebraic Varieties by Pietro Corvaja Pdf

This book is intended to be an introduction to Diophantine geometry. The central theme of the book is to investigate the distribution of integral points on algebraic varieties. This text rapidly introduces problems in Diophantine geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material. In some instances, proofs have been replaced by a detailed analysis of particular cases, referring to the quoted papers for complete proofs. A central role is played by Siegel’s finiteness theorem for integral points on curves. The book ends with the analysis of integral points on surfaces.

Author : T. N. Shorey,R. Tijdeman
Publisher : Cambridge University Press
Page : 0 pages
File Size : 43,8 Mb
Release : 2008-12-04
Category : Mathematics
ISBN : 0521091705

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Exponential Diophantine Equations by T. N. Shorey,R. Tijdeman Pdf

This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations. The necessary preliminaries are given in the first three chapters. Each chapter ends with a section giving details of related results.

Author : Jörn Steuding
Publisher : Birkhäuser
Page : 232 pages
File Size : 44,6 Mb
Release : 2016-12-21
Category : Mathematics
ISBN : 9783319488172

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Diophantine Analysis by Jörn Steuding Pdf

This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker’s method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski’s geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book.

Author : Marc Hindry,Joseph H. Silverman
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 46,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461212102

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Diophantine Geometry by Marc Hindry,Joseph H. Silverman Pdf

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Author : Michael Jacobson,Hugh Williams
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 43,8 Mb
Release : 2008-12-02
Category : Mathematics
ISBN : 9780387849225

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Solving the Pell Equation by Michael Jacobson,Hugh Williams Pdf

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.