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An Introduction To The Theory of Numbers2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

I.M.Vinogradov 著
出版社： Pergmon Press
ISBN：
出版时间：1955
标注页数：155页
文件大小：18MB
文件页数：161页
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图书目录

1 THE THEORY OF DIVISIBILITY1

1 Fundamental concepts and theorems1

2 The greatest common divisor2

3 The least common multiple5

4 The Euclidean Algorithm and continued fractions7

5 Prime numbers11

6 Uniqueness of factorization into prime factors12

Problems for Chapter 114

Numerical examples for Chapter 116

2 FUNDAMENTAL FUNCTIONS OF THE THEORY OF NUMBERS17

1 Functions [x]，{x}17

2 Summation over divisors of an integer18

3 The Moebius function19

4 Euler＇s function20

Problems for Chapter 222

Numerical examples for Chapter 230

3 CONGRUENCES31

1 Fundamental concepts31

2 Properties of congruences similar to properties of equalities32

2 Further properties of congruences34

4 Complete system of residues35

5 The reduced system of residues36

6 Theorems of Euler and Fermat37

Problems for Chapter 338

Numerical examples for Chapter 343

4 LINEAR CONGRUENCES44

1 Fundamental concepts44

2 Linear congruences44

3 Simultaneous linear congruences47

4 Congruences of any degree to a prime modulus48

5 Congruences of any degree to a composite modulus49

Problems for Chapter 452

Numerical examples for Chapter 456

5 QUADRATIC CONGRUENCES58

1 General theorems58

2 Legendre＇s symbol59

3 Jacobi＇s symbol64

4 The case of a composite modulus67

Problems for Chapter 570

Numerical examples for Chapter 575

6 PRIMITIVE ROOTS AND INDICES76

1 General theorems76

2 Primitive roots to moduli pα and 2pα76

3 Finding primitive roots to moduli pα and 2pα78

4 Indices to moduli pα and 2pα79

5 Applications of the theory of indices81

6 Indices to modulus 2α84

7 Indices to any composite modulus86

Problems for Chapter 687

Numerical examples for Chapter 693

SOLUTIONS TO PROBLEMS95

Solutions to Chapter 195

Solutions to Chapter 298

Solutions to Chapter 3111

Solutions to Chapter 4120

Solutions to Chapter 5126

Solutions to Chapter 6135

ANSWERS TO NUMERICAL EXAMPLES145

Answers to Chapter 1145

Answers to Chapter 2145

Answers to Chapter 3145

Answers to Chapter 4145

Answers to Chapter 5146

Answers to Chapter 6146

Tables of Indices148

Table of Odd Primes < 4000 and of their least primitive roots154