文档介绍：My Numbers, My
Friends:
Popular Lectures on
Number Theory
Paulo Ribenboim
Springer
My Numbers, My Friends
Paulo Ribenboim
My Numbers, My Friends
Popular Lectures on Number Theory
Paulo Ribenboim
Department of Mathematics
and Statistics
Queen’s University
Kingston, Ontario K7L 3N6
Canada
Mathematics Subject Classification (2000): 11-06, 11Axx
Library of Congress Cataloging-in-Publication Data
Ribenboim, Paulo
My numbers, my friends / Paulo Ribenboim
p. cm.
Includes bibliographical references and index.
ISBN 0-387-98911-0 (sc. : alk. paper)
1. Number Theory. I. Title
2000
612’.7— dc21 99-42458
c 2000 Springer-Verlag New York, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without
the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Av-
enue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or
scholarly analysis. Use in connection with any form of information storage and retrieval,
electronic adaptation, computer software, or by similar or dissimilar methodology now
known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication,
even if the former are not especially identified, is not to be taken as a sign that such
names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly
be used freely by anyone.
ISBN 0-387-98911-0 Springer-Verlag New York Berlin Heidelberg SPIN 10424971
Contents
Preface xi
1 The i Numbers and the Arctic Ocean 1
1 Basicdefinitions................... . 2
A. Lucassequences............... . 2
B. SpecialLucassequences............ 3
C. Generalizations................. 3
2 Basicproperties................... . 5
A. ’sformulas............... . 5
B. DegenerateLucassequences........ . 5
C. Growth and numerical calculations . . . . . 6
D. Algebraicrelations............... 7
E. Divisibility