2009;
426 pp;
Softcover

MSC: Primary 11;

**Print ISBN: 978-0-8218-4807-4
Product Code: MBK/64**

List Price: $56.00

AMS Member Price: $44.80

MAA Member Price: $50.40

**Electronic ISBN: 978-1-4704-1600-3
Product Code: MBK/64.E**

List Price: $52.00

AMS Member Price: $41.60

MAA Member Price: $46.80

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#### Supplemental Materials

# Those Fascinating Numbers

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*Jean-Marie De Koninck*

Translated by Jean-Marie De Koninck

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.

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#### Readership

Undergraduates, graduate students, and research mathematicians interested in number theory.

#### Reviews & Endorsements

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.

-- LMS Newsletter

...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

#### Table of Contents

# Table of Contents

## Those Fascinating Numbers

- Cover Cover11 free
- Title page iii5 free
- Table of contents vii9 free
- Preface ix11 free
- Notations xiii15 free
- The main functions xv17 free
- Frequently used theorems and conjectures xvii19 free
- Those fascinating numbers 121 free
- Appendix: The prime numbers <10000 409429
- Bibliography 413433
- Index 425445 free
- Back Cover Back Cover1451