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Problem-solving and selected topics in number theory : in the spirit of the mathematical olympiads

Author: Michael Th Rassias
Publisher: New York : Springer, ©2011.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is designed to introduce some of the most important theorems and results from number theory while testing the reader{u2019}s understanding through carefully selected Olympiad-caliber problems. These problems and their solutions provide the reader with an opportunity to sharpen their skills and to apply the theory. This framework guides the reader to an easy comprehension of some of the jewels of number  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michael Th Rassias
ISBN: 9781441904959 1441904956 1441904948 9781441904942
OCLC Number: 695387001
Description: 1 online resource (xiii, 324 pages)
Contents: Introduction --
The Fundamental Theorem of Arithmetic --
Arithmetic functions --
Perfect numbers, Fermat numbers --
Basic theory of congruences --
Quadratic residues and the Law of Quadratic Reciprocity --
The functions p(x) and li(x) --
The Riemann zeta function --
Dirichlet series --
Partitions of integers --
Generating functions --
Solved exercises and problems --
The harmonic series of prime numbers --
Lagrange four-square theorem --
Bertrand postulate --
An inequality for the function p(n) --
An elementary proof of the Prime Number Theorem --
Historical remarks on Fermat{u2019}s Last Theorem --
Author index --
Subject index --
Bibliography and Cited References.
Responsibility: Michael Th. Rassias ; foreword by Preda Mihăilescu.
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Abstract:

This self-contained introduction to classical number theory is written for undergraduate and graduate students, alike. Proofs of the theorems and solutions of the exercises are presented step-by-step.

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From the reviews:"Opening at random any page of this delightful book, the reader will almost certainly find something intriguing and interesting on the page. The book is an excellent "training Read more...

 
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