Diophantine Equations

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An Introduction To Diophantine Equations

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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02

An Introduction To Diophantine Equations written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Mathematics categories.

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.

Number Theory

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Author : Henri Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-23

Number Theory written by Henri Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-23 with Mathematics categories.

The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Quadratic Diophantine Equations

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Author : Titu Andreescu
language : en
Publisher: Springer
Release Date : 2015-06-29

Quadratic Diophantine Equations written by Titu Andreescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-29 with Mathematics categories.

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.

Diophantine Equations

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Author :
language : en
Publisher: Academic Press
Release Date : 1969

Diophantine Equations written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.

Diophantine Equations

Diophantus And Diophantine Equations

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Author : Isabella Grigoryevna Bashmakova
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-18

Diophantus And Diophantine Equations written by Isabella Grigoryevna Bashmakova and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-18 with categories.

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.

Solving Diophantine Equations

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Author : Octavian Cira
language : en
Publisher: Infinite Study
Release Date :

Solving Diophantine Equations written by Octavian Cira and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

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.

Diophantine Analysis

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Author : Jörn Steuding
language : en
Publisher: Birkhäuser
Release Date : 2016-12-21

Diophantine Analysis written by Jörn Steuding and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-21 with Mathematics categories.

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.

Diophantine Equations Over Function Fields

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Author : R. C. Mason
language : en
Publisher: Cambridge University Press
Release Date : 1984-04-26

Diophantine Equations Over Function Fields written by R. C. Mason and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-04-26 with Mathematics categories.

A self-contained account of a new approach to the subject.

Number Theory

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Author : Daniel Duverney
language : en
Publisher: World Scientific
Release Date : 2010

Number Theory written by Daniel Duverney and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

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. These topics are covered in 12 chapters and more than 200 solved exercises. Clear, concise, and self-contained, this textbook may be used by undergraduate and graduate students, as well as highschool mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, this fascinating branch of mathematics.

Biquadratic Diophantine Equations With Integer Solutions

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Author : Prof. Dr. M.A. Gopalan
language : en
Publisher: KY Publications
Release Date : 2018-07-01

Biquadratic Diophantine Equations With Integer Solutions written by Prof. Dr. M.A. Gopalan and has been published by KY Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-01 with Mathematics categories.

The theory of Diophantine equation is an ancient subject that typically involves solving polynomial equations in integers. It is well known that a Diophantine equation is an equation with integer coefficient and multiple variables ( 2) having integer solutions. There is no universal method available to know whether a Diophantine equation has a solutions or finding all solutions, if it exists. Proving that even simple Diophantine equations have no solutions may require very sophisticated methods and in such cases, a lot of deep and beautiful mathematics get generated as a result. It is worth to observe that Diophatine equations are rich in variety. A collection of special Problems on biquadratic equations in 3,4,5 & 6 variables has been treated in sections A to D respectively. Different sets of integer solutions to each of the biquadratic diophatine equations are illustrated.