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portada Perfect and Amicable Numbers
Type
Physical Book
Author
Publisher
Language
English
Pages
464
Format
Hardcover
Dimensions
22.9 x 15.2 x 2.5 cm
Weight
0.78 kg.
ISBN13
9789811259623
Categories

Perfect and Amicable Numbers

Elena Deza (Author) · World Scientific Publishing Company · Hardcover

Perfect and Amicable Numbers - Deza, Elena

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Synopsis "Perfect and Amicable Numbers "

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.

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