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Those Fascinating Numbers
Jean-Marie De Koninck, Université Laval, Quebec, QC, Canada
Translated by Jean-Marie De Koninck
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2009; 426 pp; softcover
ISBN-10: 0-8218-4807-0
ISBN-13: 978-0-8218-4807-4
List Price: US$49 Member Price: US$39.20
Order Code: MBK/64

Who would have thought that listing the positive integers along with their most remarkable properties could end up being such an engaging and stimulating adventure? The author uses this approach to explore elementary and advanced topics in classical number theory. A large variety of numbers are contemplated: Fermat numbers, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, voracious numbers, to name only a few. The author also presents short proofs of miscellaneous results and constantly challenges the reader with a variety of old and new number theory conjectures.

This book becomes a platform for exploring new concepts such as the index of composition and the index of isolation of an integer. In addition, the book displays several tables of particular families of numbers, including the list of all 88 narcissistic numbers and the list of the eight known numbers which are not prime powers but which can be written as the sum of the cubes of their prime factors, and in each case with the algorithm used to create them.

Reviews

"This is an unusual book. . . . It consists of a list of positive integers and some properties characterizing them, together with many interesting references which are helpful if you wish to learn more or to investigate further."

-- Jose Manuel Gamboa, European Mathematical Society

"This is a first rate resource for teachers and should certainly interest researchers. ... I loved this book and am glad I have it to play with."

"...the text is a joy...with each page and integer revealing some new delight. ... Highly recommended."

-- CHOICE Magazine

"...the author take the reader on an utmost exciting, stimulating, and adventurous voyage of exploration into the realm of classical number theory. ... Altogether, this book presents a wealth of useful and fascinating information concerning natural numbers and their various remarkable properties. It should be seen as a highly independent, but particularly lovely invitation to classical number theory, on the one hand, and as a valuable source book for active researchers in the field on the other.

"The rich bibliography containing 209 references is absolutely up-to-date and, together with the plentiful supply of complementary remarks scattered throughout the text, serves as a valuable source for further reading and exploratory attempts."

-- Zentralblatt MATH

"The book lists several thousand positive integers from 1 to Skewes number in increasing order and tells one or more interesting properties of each one. Short proofs are given for some of these properties. Many old and new open questions from classical number theory are mentioned and many references are given. The book will interest anyone who loves the natural numbers."

-- Mathematical Reviews