Diophantus And Diophantine Equations
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Diophantus And Diophantine Equations
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Author : Isabella G. Bashmakova
language : en
Publisher: Cambridge University Press
Release Date : 1997
Diophantus And Diophantine Equations written by Isabella G. Bashmakova 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 1997 with Mathematics categories.
Semi-popular maths on an area of number theory related to Fermat.
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.
Diophantus And Diophantine Equations
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Author : Isabella Grigoryevna Bashmakova
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-01-29
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 2019-01-29 with Mathematics 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.
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.
The Theory Of Numbers
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Author : Robert Daniel Carmichael
language : en
Publisher:
Release Date : 1959
The Theory Of Numbers written by Robert Daniel Carmichael and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Diophantine analysis categories.
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
History Of The Theory Of Numbers Volume Ii
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Author : Leonard Eugene Dickson
language : en
Publisher: Courier Corporation
Release Date : 2005-06-07
History Of The Theory Of Numbers Volume Ii written by Leonard Eugene Dickson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-07 with Mathematics categories.
The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms. Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.
Diophantus Of Alexandria
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Author : Thomas L. Heath
language : en
Publisher: CUP Archive
Release Date : 1910
Diophantus Of Alexandria written by Thomas L. Heath and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1910 with Algebra categories.
Unit Equations In Diophantine Number Theory
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Author : Jan-Hendrik Evertse
language : en
Publisher: Cambridge University Press
Release Date : 2015-12-30
Unit Equations In Diophantine Number Theory written by Jan-Hendrik Evertse 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 2015-12-30 with Mathematics categories.
A comprehensive, graduate-level treatment of unit equations and their various applications.
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.