An Introduction To The Theory of Numbers

1 (p1): 1 THE THEORY OF DIVISIBILITY
1 (p1-1): 1 Fundamental concepts and theorems
2 (p1-2): 2 The greatest common divisor
5 (p1-3): 3 The least common multiple
7 (p1-4): 4 The Euclidean Algorithm and continued fractions
11 (p1-5): 5 Prime numbers
12 (p1-6): 6 Uniqueness of factorization into prime factors
14 (p1-7): Problems for Chapter 1
16 (p1-8): Numerical examples for Chapter 1
17 (p2): 2 FUNDAMENTAL FUNCTIONS OF THE THEORY OF NUMBERS
17 (p2-1): 1 Functions [x]，{x}
18 (p2-2): 2 Summation over divisors of an integer
19 (p2-3): 3 The Moebius function
20 (p2-4): 4 Euler＇s function
22 (p2-5): Problems for Chapter 2
30 (p2-6): Numerical examples for Chapter 2
31 (p3): 3 CONGRUENCES
31 (p3-1): 1 Fundamental concepts
32 (p3-2): 2 Properties of congruences similar to properties of equalities
34 (p3-3): 2 Further properties of congruences
35 (p3-4): 4 Complete system of residues
36 (p3-5): 5 The reduced system of residues
37 (p3-6): 6 Theorems of Euler and Fermat
38 (p3-7): Problems for Chapter 3
43 (p3-8): Numerical examples for Chapter 3
44 (p4): 4 LINEAR CONGRUENCES
44 (p4-1): 1 Fundamental concepts
44 (p4-2): 2 Linear congruences
47 (p4-3): 3 Simultaneous linear congruences
48 (p4-4): 4 Congruences of any degree to a prime modulus
49 (p4-5): 5 Congruences of any degree to a composite modulus
52 (p4-6): Problems for Chapter 4
56 (p4-7): Numerical examples for Chapter 4
58 (p5): 5 QUADRATIC CONGRUENCES
58 (p5-1): 1 General theorems
59 (p5-2): 2 Legendre＇s symbol
64 (p5-3): 3 Jacobi＇s symbol
67 (p5-4): 4 The case of a composite modulus
70 (p5-5): Problems for Chapter 5
75 (p5-6): Numerical examples for Chapter 5
76 (p6): 6 PRIMITIVE ROOTS AND INDICES
76 (p6-1): 1 General theorems
76 (p6-2): 2 Primitive roots to moduli pα and 2pα
78 (p6-3): 3 Finding primitive roots to moduli pα and 2pα
79 (p6-4): 4 Indices to moduli pα and 2pα
81 (p6-5): 5 Applications of the theory of indices
84 (p6-6): 6 Indices to modulus 2α
86 (p6-7): 7 Indices to any composite modulus
87 (p6-8):…