Perfect And Amicable Numbers

Author : Elena Deza
Publisher : World Scientific
ISBN 13 : 981125964X
Total Pages : 462 pages
Book Rating : 4.47/5 ( download)

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Download or read book Perfect And Amicable Numbers written by Elena Deza and published by World Scientific. This book was released on 2023-02-10 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Song Y. Yan
Publisher : World Scientific
ISBN 13 : 9789810228477
Total Pages : 364 pages
Book Rating : 4.73/5 ( download)

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Download or read book Perfect, Amicable, and Sociable Numbers written by Song Y. Yan and published by World Scientific. This book was released on 1996 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : C. Edward Sandifer
Publisher : The Mathematical Association of America
ISBN 13 : 0883855844
Total Pages : 254 pages
Book Rating : 4.43/5 ( download)

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Download or read book How Euler Did Even More written by C. Edward Sandifer and published by The Mathematical Association of America. This book was released on 2014-11-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Mary Pieta Rouse
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.82/5 ( download)

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Download or read book Perfect and Amicable Numbers written by Mary Pieta Rouse and published by . This book was released on 1931 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Song Y Yan
Publisher : World Scientific
ISBN 13 : 9814498270
Total Pages : 360 pages
Book Rating : 4.72/5 ( download)

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Download or read book Perfect, Amicable And Sociable Numbers: A Computational Approach written by Song Y Yan and published by World Scientific. This book was released on 1996-09-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Martin Gardner
Publisher : American Mathematical Soc.
ISBN 13 : 147046358X
Total Pages : 302 pages
Book Rating : 4.88/5 ( download)

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Download or read book Mathematical Magic Show written by Martin Gardner and published by American Mathematical Soc.. This book was released on 2020-10-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jeffrey Stopple
Publisher : Cambridge University Press
ISBN 13 : 9780521012539
Total Pages : 404 pages
Book Rating : 4.38/5 ( download)

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Download or read book A Primer of Analytic Number Theory written by Jeffrey Stopple and published by Cambridge University Press. This book was released on 2003-06-23 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.

Author : R. Rashed
Publisher : Springer Science & Business Media
ISBN 13 : 9401732744
Total Pages : 392 pages
Book Rating : 4.41/5 ( download)

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Download or read book The Development of Arabic Mathematics: Between Arithmetic and Algebra written by R. Rashed and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history. Since the publication of the French version of these studies and of this book, its main results have been admitted by historians of Arabic mathematics, and integrated into their recent publications. This book is already a vital reference for anyone seeking to understand history of Arabic mathematics, and its contribution to Latin as well as to later mathematics. The English translation will be of particular value to historians and philosophers of mathematics and of science.

Author : James J. Tattersall
Publisher : Cambridge University Press
ISBN 13 : 9780521585316
Total Pages : 420 pages
Book Rating : 4.17/5 ( download)

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Download or read book Elementary Number Theory in Nine Chapters written by James J. Tattersall and published by Cambridge University Press. This book was released on 1999-10-14 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

Author : József Sándor
Publisher : Springer Science & Business Media
ISBN 13 : 1402042159
Total Pages : 638 pages
Book Rating : 4.57/5 ( download)

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Download or read book Handbook of Number Theory I written by József Sándor and published by Springer Science & Business Media. This book was released on 2005-11-17 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.