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Handbook of Number Theory II

Jozsef Sándor and Borislav Crstici
Publisher: 
Kluwer Academic Publishers
Publication Date: 
2004
Number of Pages: 
637
Format: 
Hardcover
Price: 
229.00
ISBN: 
1-4020-2546-7
Category: 
Handbook
[Reviewed by
S. W. Graham
, on
08/14/2005
]

This is a survey of literature on selected topics in elementary number theory. There are five chapters:

  1. Perfect numbers,
  2. Generalizations and extensions of the Möbius function,
  3. The many facets of Euler's totient,
  4. Special arithmetic functions connected with the divisors or with the digits of a number,
  5. Stirling, Bell, Bernoulli, Euler, and Eulerian numbers.

There are two approaches one can take to this project. One is typified by the book History of the Theory of Numbers, by L.E. Dickson, which is a straight reporting of the literature. The other is Unsolved Problems in Number Theory, by R. K. Guy, which strives to give an overview and a synthesis of the literature.

Both approaches have their advantages. In this book, the authors have followed Dickson's approach. Of course, they have to be more selective about their topics because the literature is much more extensive now than it was in Dickson's time.

Overall, this book should be of interest to anyone doing (or planning to do) research in elementary number theory, particularly in the topics of the chapter headings.


S. W. Graham is currently Professor of Mathematics at Central Michigan University. He can be reached at sidney.w.graham@cmich.edu.
Preface.- Basic Symbols.- Basic Notations.- Perfect Numbers: Old and New Issues: Perspectives.- Generalizations and Extensions of the M”bius Function.- The many Facets of Euler's Totient.- Special Arithmetic Function connected with the Divisors, or with the Digits of a Number.- Sterling, Bell, Bernoulli, Euler and Eulerian Numbers.- Reference.- Index.

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