Perfect And Amicable Numbers
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Perfect And Amicable Numbers
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Author : Elena Deza
language : en
Publisher: World Scientific
Release Date : 2023-02-10
Perfect And Amicable Numbers written by Elena Deza and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-10 with Mathematics categories.
This book contains a detailed presentation on the theory of two classes of special numbers, perfect numbers, and amicable numbers, as well as some of their generalizations. It also gives a large list of their properties, facts and theorems with full proofs. Perfect and amicable numbers, as well as most classes of special numbers, have many interesting properties, including numerous modern and classical applications as well as a long history connected with the names of famous mathematicians.The theory of perfect and amicable numbers is a part of pure Arithmetic, and in particular a part of Divisibility Theory and the Theory of Arithmetical Functions. Thus, for a perfect number n it holds σ(n) = 2n, where σ is the sum-of-divisors function, while for a pair of amicable numbers (n, m) it holds σ(n) = σ(m) = n + m. This is also an important part of the history of prime numbers, since the main formulas that generate perfect numbers and amicable pairs are dependent on the good choice of one or several primes of special form.Nowadays, the theory of perfect and amicable numbers contains many interesting mathematical facts and theorems, alongside many important computer algorithms needed for searching for new large elements of these two famous classes of special numbers.This book contains a list of open problems and numerous questions related to generalizations of the classical case, which provides a broad perspective on the theory of these two classes of special numbers. Perfect and Amicable Numbers can be useful and interesting to both professional and general audiences.
Perfect Amicable And Sociable Numbers
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Author : Song Y. Yan
language : en
Publisher: World Scientific
Release Date : 1996
Perfect Amicable And Sociable Numbers written by Song Y. Yan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book is about perfect, amicable and sociable numbers, with an emphasis on amicable numbers, from both a mathematical and particularly a computational point of view. Perfect and amicable numbers have been studied since antiquity, nevertheless, many problems still remain. The book introduces the basic concepts and results of perfect, amicable and sociable numbers and reviews the long history of the search for these numbers. It examines various methods, both numerical and algebraic, of generating these numbers, and also includes a set of important and interesting open problems in the area. The book is self-contained, and accessible to researchers, students, and even amateurs in mathematics and computing science. The only prerequisites are some familiarity with high-school algebra and basic computing techniques.
Perfect And Amicable Numbers
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Author : Mary Pieta Rouse
language : en
Publisher:
Release Date : 1931
Perfect And Amicable Numbers written by Mary Pieta Rouse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1931 with Number theory categories.
How Euler Did Even More
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Author : C. Edward Sandifer
language : en
Publisher: The Mathematical Association of America
Release Date : 2014-11-19
How Euler Did Even More written by C. Edward Sandifer and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
Sandifer has been studying Euler for decades and is one of the world’s leading experts on his work. This volume is the second collection of Sandifer’s “How Euler Did It” columns. Each is a jewel of historical and mathematical exposition. The sum total of years of work and study of the most prolific mathematician of history, this volume will leave you marveling at Euler’s clever inventiveness and Sandifer’s wonderful ability to explicate and put it all in context.
Prime Numbers And Perfect Numbers
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Author : School Mathematics Study Group
language : en
Publisher:
Release Date : 1966
Prime Numbers And Perfect Numbers written by School Mathematics Study Group and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Number theory categories.
History Of The Theory Of Numbers I
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Author : Leonard Eugene Dickson
language : en
Publisher: Legare Street Press
Release Date : 2023-07-22
History Of The Theory Of Numbers I written by Leonard Eugene Dickson and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-22 with categories.
A landmark work in the field of mathematics, History of the Theory of Numbers - I traces the development of number theory from ancient civilizations to the early 20th century. Written by mathematician Leonard Eugene Dickson, this book is a comprehensive and accessible introduction to the history of one of the most fundamental branches of mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Primer Of Analytic Number Theory
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Author : Jeffrey Stopple
language : en
Publisher: Cambridge University Press
Release Date : 2003-06-23
A Primer Of Analytic Number Theory written by Jeffrey Stopple 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 2003-06-23 with Mathematics categories.
An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
Mathematical Magic Show
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Author : Martin Gardner
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-06
Mathematical Magic Show written by Martin Gardner 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 2020-10-06 with Mathematics categories.
Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This volume, first published in 1977, contains columns published in the magazine from 1965-1968. This 1990 MAA edition contains a foreword by Persi Diaconis and Ron Graham and a postscript and extended bibliography added by Gardner for this edition.
Perfect Numbers And Fibonacci Sequences
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Author : Tianxin Cai
language : en
Publisher: World Scientific
Release Date : 2022-07-07
Perfect Numbers And Fibonacci Sequences written by Tianxin Cai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-07 with Mathematics categories.
In this book, we first review the history and current situation of the perfect number problem, including the origin story of the Mersenne primes, and then consider the history and current situation of the Fibonacci sequence. Both topics include results from our own research. In the later sections, we define the square sum perfect numbers, and describe for the first time the secret relationships connecting the square sum perfect numbers, the Fibonacci sequence, the Lucas sequence, the twin prime conjecture, and the Fermat primes. Throughout, we raise various interesting questions and conjectures.
Number Theory For Computing
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Author : Song Y. Yan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Number Theory For Computing written by Song Y. Yan 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 2013-11-11 with Computers categories.
This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.