最 低 价：￥169.20
定 价：￥225.55
作 者：William J. LeVeque 著 著
出 版 社：Oversea Publishing House
出版时间：2002-11-1
I S B N：9780486425399
| CHAPTER 1 INTRODUCTION 1-1 What is number theory? 1-2 Proofs 1-3 Radix representation CHAPTER 2 THE EUCLIDEAN ALGORITHM AND ITS CONSE-QUENCES 2-1 Divisibility 2-2 The Euclidean algorithm and greatest common divisor 2-3 The Unique Factorization Theorem 2-4 The linear Diophantine equation 2-5 The least common multiple CHAPTER 3 CONGRUENCES 3-1 Introduction 3-2 Elementary properties of congruences 3-3 Residue classes and Euler's q-function 3-4 Linear congruences 3-5 Congruences of higher degree 3-6 Congruences with prime moduli 3-7 The theorems of Fermat, Euler, and Wilson CHAPTER 4 PRIMITIVE I~OOTS AND INDICES 4-1 Integers belonging to a given exponent (mod p) 4-2 Primitive roots of composite moduli 4-3 Indices 4-4 An application to Fermat's conjecture CHAPTER 5 QUADRATIC RESIDUES 5-1 Introduction 5-2 Composite moduli 5-3 Quadratic residues of primes, and the Legendre symbol 5-4 The law of quadratic reciprocity 5-5 An application 5-6 The Jacobi symbol CHAPTER 6 NUMBER-THEORETIC FUNCTIONS AND THE DIS-TRIBUTION OF PRIMES 6-1 Introduction 6-2 The MSbius function 6-3 The function [x] 6-4 The symbols "0", "o", and ",~" . 6-5 The sieve of Eratosthenes 6-6 Sums involving primes 6-7 The order of (x) 6-8 Bertrand's conjecture 6-9 The order of magnitude of, a, and T 6-10 Average order of magnitude 6-11 An application CHAPTER 7 SUMS OF SQUARES 7-1 An approximation theorem 7-2 Sums of two squares 7-3 The Gaussian integers 7-4 The total number of representations 7-5 Sums of three squares 7-6 Sums of four squares CHAPTER 8 PELL'S EQUATION AND SOME APPLICATIONS 8-1 Introduction 8-2 The case N =l 8-3 The case [N]>1 8-4 An application 8-5 The minima of indefinite quadratic forms 8-6 Farey sequehces, and a proof of Hurwitz' theorem CHAPTER 9 RATIONAL APPROXIMATIONS TO REAL NUMBERS 9-1 Introduction 9-2 The rational case 9-3 The irrational case 9-4 Quadratic irrationalities 9-5 Application to Pell's equation 9-6 Equivalence of numbers SUPPLEMENTARY READING LIST OF SYMBOLS INDEX ERRATA |
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