Perfect And Amicable Numbers: 2 (Selected Chapters Of Number Theory: Special Numbers) - Hardcover

Deza, Elena

Hardcover

ISBN 10: 9811259623 ISBN 13: 9789811259623

Publisher: WSPC, 2023

Synopsis

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.

About this title

About the Author

Elena (Ivanovna) Deza has been a Full Professor at Moscow Pedagogical State University since 2006.

She wrote about 50 research papers (mainly on Number Theory and Discrete Mathematics), several mathematical textbooks and books on teaching of Mathematics in Russian, and several books/monographs in English, including: Deza E, Deza M M (2006) Dictionary of Distances, Elsevier; Deza E, Deza M M (2009, 2013, 2015, 2016) Encyclopedia of Distances, Springer Verlag; Deza E, Deza M M (2012) Figurate Numbers, World Scientific Publishing Company; Deza E, Deza M M, Dutour Siciric M (2016) Generalizations of Finite Metrics and Cuts, World Scientific Publishing Company; Deza E Mersenne Numbers and Fermat Numbers (2021) World Scientific Publishing Company.

One of her special courses at Moscow State Pedagogical and Moscow Independent Universities is "Topics in Special Numbers". Her mathematical teaching publications are mainly in the following leading Russian journals: Mathematics in School (about 20 papers, including 4 surveys on special numbers), Kvant (10 papers) and Vestnik of University of Russian Academy of Education. Also, she published 9 mathematical textbooks in Russian.

Research track records of Elena Deza are: Analytic Number Theory (Dirichlet Divisor problem, Dirichlet series, Theory of the Riemann zeta function, mean values of arithmetical functions); Discrete Mathematics (Combinatorics, Graph Theory, Special Integer Numbers); Theory of Discrete Metric Spaces (Oriented Metrics, m-metrics, Partial Metrics); Problems of Mathematical Education (Higher Pedagogical Education, Multilevel System of Pedagogical Education, Training of School Students).

Edition details

• Publisher: WSPC
• Publication date: 2023
• Language: English
• ISBN 10: 9811259623
• ISBN 13: 9789811259623
• Binding: Hardcover
• Number of pages: 462