Cover of: Theory of Numbers | Amin Witno

Theory of Numbers

1st ed.

Published by BookSurge in North Charleston, SC .
Written in English

About the Edition

Theory of Numbers is a carefully written textbook for an elementary number theory course with minimal prerequisites. It begins with the classical theory of divisibility, primes, and modular arithmetic; and ends with computational topics of factorization, pseudoprimes, and primality testing. Ideal for self-study or for a one-semester course, the relatively small, measured contents include numerous exercises strategically dispersed throughout the text in order to retain theoretical context and reinforce understanding. As an extended workout, every chapter concludes with a partially guided project touching on a wide range of problems, from the old sums-of-squares theorems to the more recent cryptographical protocols.

Table of Contents

1 Divisibility 1
2 Prime Numbers 12
3 Modular Arithmetic 21
4 Exponentiation 31
5 Primitive Roots 43
6 Quadratic Residues 52
7 Factorization 63
8 Pseudoprime Composites 74
9 Primality Proving 84
A Mathematical Induction 96
B Binomial Coefficients 98
C Primitive Root Theorem 101
D Modular Square Roots 103
E Rabin's Probabilistic Test 108
F Testing Primes with Lucas Sequences 110
Answers & Hints 115
Primes < 10^4 124
Pseudoprimes < 10^7 127
Bibliography 130
Notation 133
Index 134

Edition Notes

Includes bibliographical references (p. 130-132) and index.


Library of Congress
QA241 .W635 2008

The Physical Object

viii, 136 p. :
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