文档介绍：Elementary Number Theory
in Nine Chapters
Second Edition
To Terry
JAMES J. TATTERSALL
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge ,UK
Published in the United States of America by Cambridge University Press, New York
Information on this title: /9780521850148
© Cambridge University Press 2005
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Contents
Preface page ix
1 The intriguing natural numbers
Polygonal numbers 1
Sequences of natural numbers 23
The principle of mathematical induction 40
Miscellaneous exercises 43
Supplementary exercises 50
2 Divisibility
The division algorithm 55
The mon divisor 64
The Euclidean algorithm 70
Pythagorean triples 76
Miscellaneous exercises 81
Supplementary exercises 84
3 Prime numbers
Euclid on primes 87
Number theoretic functions 94
Multiplicative functions 103
Factoring 108
The greatest integer function 112
Primes revisited 115
Miscellaneous exercises 129
Supplementary exercises 133
vi
Contents vii
4 Perfect and amicable numbers
Perfect numbers 136