Some Congruence Properties Of Pell S Equation
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Some Congruence Properties Of Pell S Equation
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Author : Nathan C. Priddis
language : en
Publisher:
Release Date : 2009
Some Congruence Properties Of Pell S Equation written by Nathan C. Priddis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Electronic dissertations categories.
In this thesis I will outline the impact of Pell's equation on various branches of number theory, as well as some of the history. I will also discuss some recently discovered properties of the solutions of Pell's equation.
Solving The Pell Equation
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Author : Michael Jacobson
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-04
Solving The Pell Equation written by Michael Jacobson 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 2008-12-04 with Mathematics categories.
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.
The Pell Equation
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Author : Edward Everett Whitford
language : en
Publisher:
Release Date : 2008
The Pell Equation written by Edward Everett Whitford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
An Unabridged, Digitally Enlarged History Of The Equation; Table Of Solutions From A = 1,5001 To A = 1,700, Bibliography With References To Over 300 Authors, and Table Of Continued Fractions For Square Root Of A.
On The Multiple Solutions Of The Pell Equation
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Author : Derrick Henry Lehmer
language : en
Publisher:
Release Date : 1929*
On The Multiple Solutions Of The Pell Equation written by Derrick Henry Lehmer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1929* with Diophantine analysis categories.
Pell S Equation
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Author : Edward J Barbeau
language : en
Publisher:
Release Date : 2003-01-14
Pell S Equation written by Edward J Barbeau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-14 with categories.
Pell And Pell Lucas Numbers With Applications
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Author : Thomas Koshy
language : en
Publisher: Springer
Release Date : 2014-11-11
Pell And Pell Lucas Numbers With Applications written by Thomas Koshy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-11 with Mathematics categories.
Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences. A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book. Finally, Pell and Pell–Lucas Numbers provides enjoyment and excitement while sharpening the reader’s mathematical skills involving pattern recognition, proof-and-problem-solving techniques.
Pell S Equation
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Author : Edward J. Barbeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-04
Pell S Equation written by Edward J. Barbeau 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 2006-05-04 with Mathematics categories.
Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical technique. Even at the specific level of quadratic diophantine equations, there are unsolved problems, and the higher degree analogues of Pell's equation, particularly beyond the third, do not appear to have been well studied. In this focused exercise book, the topic is motivated and developed through sections of exercises which will allow the readers to recreate known theory and provide a focus for their algebraic practice. There are several explorations that encourage the reader to embark on their own research. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.
Computability Complexity Logic
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Author : E. Börger
language : en
Publisher: Elsevier
Release Date : 1989-07-01
Computability Complexity Logic written by E. Börger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-01 with Mathematics categories.
The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems. The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory. It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.
T Hoku Mathematical Journal
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Author :
language : en
Publisher:
Release Date : 1921
T Hoku Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1921 with Mathematics categories.
Quadratic Number Fields
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Author : Franz Lemmermeyer
language : en
Publisher: Springer Nature
Release Date : 2021-09-18
Quadratic Number Fields written by Franz Lemmermeyer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-18 with Mathematics categories.
This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.