Exponential 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.

Exponential Diophantine Equations

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Author : T. N. Shorey
language : en
Publisher:
Release Date : 1986

Exponential Diophantine Equations written by T. N. Shorey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Diophantine analysis categories.

Diophantine Equations

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Author : Sudhanshu Aggarwal
language : en
Publisher: Independently Published
Release Date : 2021-08-18

Diophantine Equations written by Sudhanshu Aggarwal and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-18 with categories.

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

Some Exponential Diophantine Equations

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Author : Nobuhiro Terai
language : en
Publisher:
Release Date : 1993

Some Exponential Diophantine Equations written by Nobuhiro Terai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

Exponential Diophantine Equations With Four Terms

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Author : Mo Deze
language : en
Publisher:
Release Date : 1991

Exponential Diophantine Equations With Four Terms written by Mo Deze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.

Random Reals And Exponential Diophantine Equations

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Author : G. J. Chaitin
language : en
Publisher:
Release Date : 1986

Random Reals And Exponential Diophantine Equations written by G. J. Chaitin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

Algorithms For Diophantine Equations

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Author : Benne M. M. De Weger
language : en
Publisher:
Release Date : 1989

Algorithms For Diophantine Equations written by Benne M. M. De Weger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Algebra categories.

Exponential Diophantine Equations

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Author : T. N. Shorey
language : en
Publisher: Cambridge University Press
Release Date : 2008-12-04

Exponential Diophantine Equations written by T. N. Shorey 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 2008-12-04 with Mathematics categories.

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.

Solving Exponential Diophantine Equations Using Lattice Basis Reduction Algorithms

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Author : B. M. M. de Weger
language : en
Publisher:
Release Date : 1986

Solving Exponential Diophantine Equations Using Lattice Basis Reduction Algorithms written by B. M. M. de Weger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.

Understanding Anatomy Of Exponential Diophantine 3 Term Equations

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Author : Rajen Merchant
language : en
Publisher:
Release Date : 2020-09-28

Understanding Anatomy Of Exponential Diophantine 3 Term Equations written by Rajen Merchant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with categories.

This monograph is specially written for students and researchers in mathematics, particularly number theory. Professors and instructors teaching this subject will find it very useful. This monograph develops a clear understanding of the structure of the exponential diophantine 3-term equations and their solutions. Various components of an exponential diophantine equation and their roles are described in detail. A combinatorial approach is used to classify and analyze solutions to exponential diophantine 3-term equations. To classify these solutions, all possible ways these solutions can occur are examined. The analysis presented reveals that these solutions can be classified into three classes and six sub-classes. Properties of each class of solutions are described in detail. We observe that each exponential diophantine 3-term equation imposes its own requirements on its solutions. We discuss how these requirements of an exponential diophantine equation can affect solutions in each class. We apply the classification developed here to relate to the results for the Pythagorean equation, the Catalan equation, and the Ramanujan-Nagell equation. Finally, we employ the concepts developed in this monograph and present twelve proofs and four conjectures that help us analyze and understand the Fermat's Last Theorem and the Beal's conjecture. These four conjectures are much smaller in scope.