My Numbers, My Friends - Popular Lectures on Number Theory.pdf

(1627 KB) Pobierz
136572534 UNPDF
My Numbers, My Friends
136572534.001.png
Paulo Ribenboim
My Numbers, My Friends
Popular Lectures on Number Theory
136572534.002.png
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
QA241.R467 2000
612’.7— dc21
99-42458
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
c
136572534.003.png
Contents
Preface
xi
1 The Fibonacci Numbers and the Arctic Ocean 1
1 Basicdefinitions ................... . 2
A. Lucassequences ............... . 2
B. SpecialLucassequences........... . 3
C. Generalizations................ . 3
2 Basicproperties ................... . 5
A. Binet’sformulas ............... . 5
B. DegenerateLucassequences ........ . 5
C. Growth and numerical calculations . . . . . 6
D. Algebraicrelations.............. . 7
E.
Divisibility properties ............ . 9
3
Prime divisors of Lucas sequences ......... . 10
A.
( V ), and the rank of
appearance................... . 10
B. Primitive factors of Lucas sequences . . . . 17
4 PrimesinLucassequences ............. . 26
5
The sets
P
( U ),
P
Powers and powerful numbers in Lucas sequences . 28
A. Generaltheoremsforpowers........ . 29
B.
Explicit determination in special sequences . 30

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin