Exponential Diophantine Equations

Exponential Diophantine Equations PDF

Author: T. N. Shorey

Publisher: Cambridge University Press

Published: 2008-12-04

Total Pages: 0

ISBN-13: 9780521091701

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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.

Exponential Diophantine Equations

Exponential Diophantine Equations PDF

Author: T. N. Shorey

Publisher: Cambridge University Press

Published: 1986-11-27

Total Pages: 256

ISBN-13: 9780521268264

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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.

Exponential Diophantine Equations

Exponential Diophantine Equations PDF

Author: T. N. Shorey

Publisher: Cambridge University Press

Published: 1986-11-27

Total Pages: 256

ISBN-13: 9780521268264

DOWNLOAD EBOOK →

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.

An Introduction to Diophantine Equations

An Introduction to Diophantine Equations PDF

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2010-09-02

Total Pages: 350

ISBN-13: 0817645497

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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.

Notes from the International Autumn School on Computational Number Theory

Notes from the International Autumn School on Computational Number Theory PDF

Author: Ilker Inam

Publisher: Springer

Published: 2019-04-17

Total Pages: 363

ISBN-13: 3030125580

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This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include: Modular forms L-functions The modular symbols algorithm Diophantine equations Nullstellensatz Eisenstein series Notes from the International Autumn School on Computational Number Theory will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the-art of the field, and will thus be of interest to researchers interested in the field as well.

Diophantine Equations

Diophantine Equations PDF

Author: Sudhanshu Aggarwal

Publisher: Independently Published

Published: 2021-08-18

Total Pages: 66

ISBN-13:

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The present book "Diophantine Equations" is presented for students and researchers working in the field of number theory. Diophantine equations are those equations which are to be solved in integers. Diophantine equations are very important equations of theory of numbers and have many important applications in algebra, analytical geometry and trigonometry. The present book describes various methods for handling Diophantine equations. The present book is divided into five chapters. 1. ON THE NON-LINEAR DIOPHANTINE EQUATION 79x+97y=z2 (Nidhi Sharma, Shahida A.T., Renu Chaudhary) 12-23 2. ON THE EXPONENTIAL DIOPHANTINE EQUATION M3p+M7q=r2 (Sanjay Kumar, Aakansha Vyas, Gyanvendra Pratap Singh) 24-31 3. ON THE SOLUTIONS OF EXPONENTIAL DIOPHANTINE EQUATION kx + (k + 10)y= z2 (Deepak Gupta) 32-41 4. DIOPHANTINE EQUATION 787x+797y=z2 (Raman Chauhan, Swarg Deep Sharma, Seema Agrawal) 42-48 5. DIOPHANTINE EQUATIONS α2-Dβ2=1 ANDα2-Dβ2=-1 (Sudhanshu Aggarwal, Rajesh Pandey, Eshita Pandey) 49-64 Dr. Sudhanshu Aggarwal Dr. Himanshu Pandey Dr. Satish Kumar Dr. Anjana Rani Gupta

Solving the Pell Equation

Solving the Pell Equation PDF

Author: Michael Jacobson

Publisher: Springer Science & Business Media

Published: 2008-12-02

Total Pages: 504

ISBN-13: 038784922X

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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.

Diophantine Approximation on Linear Algebraic Groups

Diophantine Approximation on Linear Algebraic Groups PDF

Author: Michel Waldschmidt

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 649

ISBN-13: 3662115697

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The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

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