文档介绍：Benjamin Fine
Gerhard Rosenberger
Number Theory
An Introduction via the
Distribution of Primes
Birkhauser¨
Boston • Basel • Berlin
Benjamin Fine Gerhard Rosenberger
Fairfield University Universitat¨ Dortmund
Department of Mathematics Fachbereich Mathematik
Fairfield, CT 06824 D-44221 Dortmund
. Germany
Cover design by Alex Gerasev.
Mathematics Subject Classification (2000): 11A01, 11A03, 11M01, 11R01, 11Z05, 11T71, 11H01,
20A01, 20G01, 20K01, 14G01, 08A01
Library of Congress Control Number: 2006931568
ISBN-10 0-8176-4472-5 e-ISBN-10 0-8176-4545-1
ISBN-13 978-0-8176-4472-7 e-ISBN-13 978-0-8176-4541-0
Printed on acid-free paper.
c 2007 Birkhauser¨ Boston
All rights reserved. This work may not be translated or copied in whole or in part without the written
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987654321
(TXQ/EB)
To our families:
Linda, Carolyn, David, Scott, Shane, and Sawyer,
Katariina, Anja, and Aila
Contents
Preface ......................................................... xi
1 Introduction and Historical Remarks............................ 1
2 Basic Number Theory ......................................... 7
The Ring of Integers ........................................ 7
Divisibility, Primes, posites .......................... 11
The Fundamental Theorem of Arithmetic ....................