Diophantine Equations And Systems
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Diophantine Equations And Systems
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Author : Demetrios P Kanoussis Ph D
language : en
Publisher: Independently Published
Release Date : 2024-03-08
Diophantine Equations And Systems written by Demetrios P Kanoussis Ph D and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-08 with Mathematics categories.
Diophantine equations are polynomial equations with integer coefficients for which only integer solutions are sought. In his great work "Arithmetica", the Greek mathematician Diophantus of Alexandria, (born in Alexandria Egypt in 200 AD and died in 284 AD), known as the father of Algebra, studied and solved such types of equations, (integer coefficients and integer solutions), of the first up to the fourth degree. These equations are now known as "Diophantine equations". A characteristic feature of Diophantine equations is that in these equations the number of equations is smaller than the number of unknowns. For example, we may have one equation with two unknowns, or one equation with three unknowns, or a system of two equations with three unknowns, etc. While in the set of real numbers R these types of equations, (fewer equations than number of unknowns), are indeterminate, in the set of integers Z={... -3, -2, -1,0,1,2,3, ...} or in the set of natural numbers N={1,2,3,4, ...}, these equations may or may not have integer solutions, (depending on the coefficients of the equations). In this book we provide a systematic introduction to Diophantine equations, with emphasis on the solution of various problems. The first two chapters are devoted to first degree Diophantine equations and systems, (linear equations and systems), while the third chapter is devoted to second degree Diophantine equations and systems. Among other equations, in this chapter, we study the Pythagorean equation (x^2+y^2=z^2), and the Pell's equation (x^2-ky^2=1). The solution of Pell's equation is achieved by a really brilliant method, which is attributed to Lagrange. Various examples of higher degree Diophantine equations are considered in chapter 4. The analytic description of the material covered in this book can be found in the table of contents. The book is concluded with a collection of 40 miscellaneous, challenging problems, with answers and detailed remarks and hints. In total, the book contains 55 solved examples and 105 problems for solution.
A Study Of Linear Diophantine Equations And Systems Of Linear Diophantine Equations
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Author : John Owen Ethridge
language : en
Publisher:
Release Date : 1950
A Study Of Linear Diophantine Equations And Systems Of Linear Diophantine Equations written by John Owen Ethridge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Diophantine analysis categories.
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.
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 : 2008-10-10
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 2008-10-10 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.
Algorithms For The Solution Of Systems Of Linear Diophantine Equations
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Author : Joseph Tsu-wu Chou
language : en
Publisher:
Release Date : 1979
Algorithms For The Solution Of Systems Of Linear Diophantine Equations written by Joseph Tsu-wu Chou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Diophantine analysis categories.
Mathematical Foundations Of Computer Science 1991
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Author : Andrzej Tarlecki
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-08-07
Mathematical Foundations Of Computer Science 1991 written by Andrzej Tarlecki 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 1991-08-07 with Computers categories.
This volume contains the proceedings of the 16th International Symposium on Mathematical Foundations of Computer Science, MFCS '91, held in Kazimierz Dolny, Poland, September 9-13, 1991. The series of MFCS symposia, organized alternately in Poland and Czechoslovakia since 1972, has a long and well established tradition. The purpose of the series is to encourage high-quality research in all branches of theoretical computer science and to bring together specialists working actively in the area. Principal areas of interest in this symposium include: software specification and development, parallel and distributed computing, logic and semantics of programs, algorithms, automata and formal languages, complexity and computability theory, and others. The volume contains 5 invited papers by distinguished scientists and 38 contributions selected from a total of 109 submitted papers.
Number Theory
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Author : Henri Cohen
language : en
Publisher: Springer
Release Date : 2007-05-23
Number Theory written by Henri Cohen and has been published by Springer 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.
Algorithms For The Solution Of Systems Of Linear Diophantine Equations
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Author : Tsu-Wu J. Chou
language : en
Publisher:
Release Date : 1981
Algorithms For The Solution Of Systems Of Linear Diophantine Equations written by Tsu-Wu J. Chou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Neutrosophic Linear Diophantine Equations With Two Variables
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Author : Hasan Sankari
language : en
Publisher: Infinite Study
Release Date : 2020-12-01
Neutrosophic Linear Diophantine Equations With Two Variables written by Hasan Sankari and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Mathematics categories.
This paper is devoted to study for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers. This work introduces an algorithm to solve the linear Diophantine equation.