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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.
Contents:
- Concepts and History
- Mathematical Tools
- Exhaustive Numerical Methods
- Algebraic Assumption Methods
- Algebraic Constructive Methods
- Conclusions and Open Problems
Readership: Researchers, students and even amateurs in mathematics and computing science.
“… this book is fascinating and eminently readable. I can strongly recommend it.”
The Mathematical Gazette
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