Induction and Recursion
Almost all of part I of this book belongs to elementary number theory (ENT). This notion can be rigorously defined using tools of mathematical logic, but in order to do this one must first introduce a formal language of arithmetic and fix an adopted syste
- PDF / 28,927,857 Bytes
- 311 Pages / 439.37 x 666.142 pts Page_size
- 14 Downloads / 262 Views
Editor-in-Chief: R.Y. Gamkrelidze
Springer-Verlag Berlin Heidelberg GmbH
A. N. Parshin I. R. Shafarevich (Eds.)
Number Theory I Fundamental Problems, Ideas and Theories
With 17 Figures
Springer
Consulting Editors of the Series: AA Agrachev, AA Gonchar, E.F. Mishchenko, N.M. Ostianu, V.P. Sakharova, AB. Zhishchenko
Title of the Russian edition: Itogi nauki i tekhniki, Sovremennye problemy matematiki , FundamentaI'nye napravleniya, Vol. 49, Teoriya chisel 1 Publisher VINITI, Moscow 1990
LIbrary of Congress CatalogIng-In-PublIcatIon Data Teorlfa ch i s el 1. English Number theory I : fundamental problems, Ideas, and theories / A.N. Parshln. I .R. Shafarevl ch, eds. p. cm . -- (Encyclopaedia of mathematical scIences: v . 49) Issued orIginally as : Teorlra ch isel I, v , 49 of the serial : !togl I nauk 1. Serl fa Sovremennye problemy matematlk 1. Fundamenta I 'nve naprav Ien I fa. Includes bibliographical references and Index . 1. Number theory. I . Parshln, A. N. II. Shafarevlch. I . R. (Igor Rostlslavovlch). 1923III. Title . IV. Title : Number theory one . V. Series . QA241 .T43313 1995 94-46819 512 ' .72--dc20 CIP
Mathematics Subject Classification (1991): 11-02, l IAxx, IIBxx, l IDxx, llExx, l LFxx, l IGxx , l IRxx, l l Sxx, l IVxx, l l Txx, I1Yxx, llZ05, 14Gxx, 14H52, 14120, 14K15, 19F27, 20Gxx, 32Nxx
ISBN 978-3-662-08007-8 ISBN 978-3-662-08005-4 (eBook) DOI 10.1007/978-3-662-08005-4
This work is subject to copyright. All rights are reserved . whether the whole or part of the material is concerned. specifically the rights of translation . reprinting. reuse of illustrations. recitation. broadcasting. reproduction on microfilm or in any other way. and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9. 1965. in its current version. and permission for use must always be obtained from Springer. Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1995
Originally published by Springer-Verlag Berlin Heidelberg New York in 1995. Softcover reprint of the hardcover 1st edition 1995 Typesetting : Camera-ready copy from the translator using a Springer TEX macro package SPIN: 10020191 41/3142 - 5 432 I O· Printed on acid-free paper
List of Editors and Authors Editor-in-Chief
R. V. Gamkrelidze, Russian Academy of Sciences, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Institute for Scientific Information (VINITI), ul. Usievicha 20a, 125219 Moscow, Russia, e-mail: [email protected]
Consulting Editors A. N. Parshin, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Russia, e-mail : [email protected] I. R. Shafarevich, Steklov Mathematical Institute, ul. Vavilova 42, 117966 Moscow, Russia
Authors and Translators Yu. I. Manin, Max-Planck-Institut fur Mathematik, Gottfried-Claren-Str. 26, 53225 Bonn, e-mail: [email protected] A. A. Panchishkin, Institut Fourier, Universite Grenoble I, Laboratoire Math. Pu
