International Series in Pure and Applied Mathematics Ahlfors: Complex Analysis Bender and Orszag: Advanced Mathematical...

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International Series in Pure and Applied Mathematics Ahlfors: Complex Analysis Bender and Orszag: Advanced Mathematical Methods for Scientists and Engineers Bilodeau and Thie: An Introduction to Analysis Boas: Invitation to Complex Analysis Brown and Churchill: Complex Variables and Applications Brown and Churchill: Fourier Series and Boundary Value Problems Buchanan and Turner: Numerical Methods and Analysis Buck: Advanced Calculus Burton: Elementary Number Theory Burton: The History ofMathematics: An Introduction Chartrand and Oellermann: Applied and Algorithmic Graph Theory Colton: Partial Differential Equations Conte and de Boor: Elementary Numerical Analysis: An Algorithmic Approach Edelstein-Keshet: Mathematical Models in Biology Farlow: An Introduction to Differential Equations and Their Applications Goldberg: Matrix Theory with Applications Gulick: Encounters with Chaos Hill: Experiments in Computational Matrix Algebra Keisler and Robbin: Mathematical Logic and Computability Kurtz: Foundations ofAbstract Mathematics Lewin and Lewin: An Introduction to Mathematical Analysis Malik, Mordeson, & Sen: Fundamentals ofAbstract Algebra Morash: Bridge to Abstract Mathematics: Mathematical Proof and Structures Parzynski and Zipse: Introduction to Mathematical Analysis Pinsky: Partial Differential Equations and Boundary- Value Problems Pinter: A Book ofAbstract Algebra Ralston and Rabinowitz: A First Course in Numerical Analysis Ritger and Rose: Differential Equations with Applications Robertson: Engineering Mathematics with Maple Robertson: Engineering Mathematics with Mathematica Rudin: Functional Analysis Rudin: Principles ofMathematical Analysis Rudin: Real and Complex Analysis Schcick: Linear Algebra with Applications Simmons: Differential Equations with Applications and Historical Notes Small and Hosack: Calculus: An Integrated Approach Small and Hosack: Explorations in Calculus with a Computer Algebra System Vanden Eynden: Elementary Number Theory Walker: Introduction to Abstract Algebra

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ELEMENTARY NUMBER THEORY, FIFTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2002, 1998, 1997, 1995, 1991 by The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOC / DOC 0 9 8 7 6 5 4 3 2 1 ISBN 0-07-232569-0 ISBN 0-07-112174-9 (ISE) Publisher: William K. Barter Senior sponsoring editor: Maggie Rogers Editorial coordinator: Allyndreth Cassidy Marketing manager: Mary K. Kittell Project manager: Sheila M. Frank Lead production supervisor: Sandra Hahn Designer: K. Wayne Harms Cover designer: Nathan Bahls Photo research coordinator: John C. Leland Senior supplement producer: Stacy A. Patch Media technology lead producer: Steve Metz Compositor: Techsetters, Inc. Typeface: 10.5/12 Times Roman Printer: R. R. Donnelley & Sons Company/Crawfordsville, IN

Library of Congress Cataloging-in-Publication Data Burton, David M. Elementary number theory / David M. Burton.-5th ed. cm.-(International series in pure and applied mathematics) p. Includes bibliographical references and index. ISBN 0-07-232569-0 1. Number theory. I. Title. II. Series. QA241 .B83 2002 512' .72-dc21

2001030785 CIP

INTERNATIONAL EDITION ISBN 0-07-112174-9 Copyright © 2002. Exclusive rights by The McGraw-Hill Companies, Inc., for manufacture and export. This book cannot be re-exported from the country to which it is sold by McGraw-Hill. The International Edition is not available in North America.