Elementary Number Theory

Title
Preface
Contents
1. Rules of the Game
1.1 The Integers
1.2 Well-Ordering
1.3 Induction
Exercises
2. Divisibility
2.1 Division
2.2 Greatest Common Divisors
2.3 The Equation aX + bY = c
Exercises
3. Prime Numbers
3.1 Primes
3.2 A Sieve Method
3.3 Fermat Factorization
3.4 Some Unsolved Problems
Exercises
4. Congruences
4.1 Congruence
4.2 Inverses Modulo m
4.3 Fermat’s Little Theorem
4.4 Euler’s Theorem
4.5 A Historical View
4.6 Wilson’s Theorem
Exercises
5. Multiplicative Functions
5.1 Three Special Functions
5.2 Perfect Numbers
5.3 Möbius Inversion
Exercises
6. Solving Congruences
6.1 The Congruence aX equiv b mod m
6.2 Systems of Linear Congruences
6.3 The Congruence X^2 equiv a mod m
6.4 A General Theorem
Exercises
7. Sums of Squares
7.1 Pythagorean Triples
7.2 Sums of Two Squares
7.3 Sums of Four Squares
Exercises
8. Primitive Roots
Exercises
9. Quadratic Reciprocity
9.1 The Legendre Symbol
9.2 The Quadratic Reciprocity Theorem
Exercises
Tables
Index