Introduction to Number Theory (Reprint)

to Number Theory Translated from the Chinese by Peter Shiu With 14 Figures Springer-Verlag Berlin Heidelberg New York 1982 HuaLooKeng Institute of Mathematics Academia Sinica Beijing The People's Republic of China PeterShlu Department of Mathematics University of Technology Loughborough Leicestershire LE 11 3 TU United Kingdom ISBN -13 : 978-3-642-68132-5 e-ISBN -13 : 978-3-642-68130-1 DOl: 10.1007/978-3-642-68130-1 Library of Congress Cataloging in Publication Data. Hua, Loo-Keng, 1910 -. Introduc tion to number theory. Translation of: Shu lun tao yin. Bibliography: p. Includes index. 1. Numbers, Theory of. I. Title. QA241.H7513.5 12'.7.82-645. ISBN-13:978-3-642-68132-5 (U.S.). AACR2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustra tions, broadcasting, reproductiOli by photocopying machine or similar means, and storage in data banks. Under
54 of the German Copyright Law where copies are made for other than private use a fee is payable to "VerwertungsgeselIschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1982 Softcover reprint of the hardcover 1st edition 1982 Typesetting: Buchdruckerei Dipl.-Ing. Schwarz' Erben KG, Zwettl. 214113140-5432 I 0 Preface to the English Edition The reasons for writing this book have already been given in the preface to the original edition and it suffices to append a few more points. 1. The Factorization of Integers.- 2. Congruences.- 3. Quadratic Residues.- 4. Properties of Polynomials.- 5. The Distribution of Prime Numbers.- 6. Arithmetic Functions.- 7. Trigonometric Sums and Characters.- 8. On Several Arithmetic Problems Associated with the Elliptic Modular Function.- 9. The Prime Number Theorem.- 10. Continued Fractions and Approximation Methods.- 11. Indeterminate Equations.- 12. Binary Quadratic Forms.- 13. Unimodular Transformations.- 14. Integer Matrices and Their Applications.- 15. p-adic Numbers.- 16. Introduction to Algebraic Number Theory.- 17. Algebraic Numbers and Transcendental Numbers.- 18. Waring's Problem and the Problem of Prouhet and Tarry.- 19. Schnirelmann Density.- 20. The Geometry of Numbers.