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ISBN 10: 0321538013
ISBN 13: 9780321538017
Author: Kenneth H Rosen
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Reproduced by Pearson Addison-Wesley from electronic files supplied by the author. Copyright © 2011, 2005, 2000 Pearson Education, Inc. Publishing as Addison-Wesley, 75 Arlington Street, Boston, MA 02116. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.
Chapter 1. The Integers
• 1.1 Numbers and Sequences
• 1.2 Sums and Products
• 1.3 Mathematical Induction
• 1.4 The Fibonacci Numbers
• 1.5 Divisibility
Chapter 2. Integer Representations and Operations
• 2.1 Representations of Integers
• 2.2 Computer Operations with Integers
• 2.3 Complexity and Integer Operations
Chapter 3. Primes and Greatest Common Divisors
• 3.1 Prime Numbers
• 3.2 The Distribution of Primes
• 3.3 Greatest Common Divisors and their Properties
• 3.4 The Euclidean Algorithm
• 3.5 The Fundamental Theorem of Arithmetic
• 3.6 Factorization Methods and the Fermat Numbers
• 3.7 Linear Diophantine Equations
Chapter 4. Congruences
• 4.1 Introduction to Congruences
• 4.2 Linear Congruences
• 4.3 The Chinese Remainder Theorem
• 4.4 Solving Polynomial Congruences
• 4.5 Systems of Linear Congruences
• 4.6 Factoring Using the Pollard Rho Method
Chapter 5. Applications of Congruences
• 5.1 Divisibility Tests
• 5.2 The Perpetual Calendar
• 5.3 Round-Robin Tournaments
• 5.4 Hashing Functions
• 5.5 Check Digits
Chapter 6. Some Special Congruences
• 6.1 Wilson’s Theorem and Fermat’s Little Theorem
• 6.2 Pseudoprimes
• 6.3 Euler’s Theorem
Chapter 7. Multiplicative Functions
• 7.1 The Euler Phi-Function
• 7.2 The Sum and Number of Divisors
• 7.3 Perfect Numbers and Mersenne Primes
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Tags: Kenneth H Rosen, Elementary, Theory
