Elements of number theory

Cover
Title page
Preface
Chapter I DIVISIBILITY THEORY
l. Basic Concepts and Theorems
2. The Greatest Common Divisor
3. The Least Common Multiple
4. The Relation of Euc!id's Aigorithm to Continued Fractions
5. Prime Numbers
6. The Unicity of Prime Decomposition
Problems for Chapter I
Numerical Exercises for Chapter I
Chapter II IMPORTANT NUMBER THEORETICAL FUNCTIONS
1. The Functions {x}, x
2. Sums Extended over the Divisors of a Number
3. The Möbius Function
4. The Euler Function
Problems for Chapter II
Numerical Exercises for Chapter II
Chapter III CONGRUENCES
l. Basic Concepts
2. Properties of Congruences Similar to those of Equations
3. Further Properties of Congruences
4. Complete Systems of Residues
5. Reduced Systems of Residues
6. The Theorems of Euler and Fermat
Problems for Chapter III
Numerical Exercises for Chapter III
Chapter IV CONGRUENCES IN ONE UNKNOWN
l. Basic Concepts
2. Congruences of the First Degree
3. Systems of Congruences of the First Degree
4. Congruences of Arbitrary Degree with Prime Modulus
5. Congruences of Arbitrary Degree with Composite Modulus
Problems for Chapter IV
Numerical Exercises for Chapter IV
Chapter V CONGRUENCES OF SECOND DEGREE
l. General Theorems
2. The Legendre Symbol
3. The Jacobi Symbol
4. The Case of Composite Moduli
Problems for Chapter V
Numerical Exercises for Chapter V
Chapter VI PRIMITIVE ROOTS AND INDICES
l. General Theorems
2. Primitive Roots Modulo p^a and 2p^a
3. Evaluation of Primitive Roots for the Moduli p^a and 2p^a
4. Indices for the Moduli p^a and 2p^a 1l0
5. Consequences of the Preceding Theory
6. Indices Modulo 2^a 1l6
7. Indices for Arbitrary Composite Modulus
Problems for Chapter VI
Numerical Exercises for Chapter VI
SOLUTIONS OF THE PROBLEMS
Solutions for Chapter I
Solutions for Chapter II
Solutions for Chapter III
Solutions for Chapter IV
Solutions for Chapter V
Solutions for Chapter VI
ANSWERS TO THE NUMERICAL EXERCISES
Answers for Chapter I
Answers for Chapter II
Answers for Chapter III
Answers for Chapter IV
Answers for Chapter V
Answers for Chapter VI
TABLES OF INDICES
TABLES OF PRIMES < 4000 AND THEIR LEAST PRIMITIVE ROOTS