Author(s): Efraim P. Armendáriz, Stephen J. McAdam
Publisher: MacMillan
Year: 1980
Language: English
City: New York
Chapter 1
Rules of the Game
1
1
. 1 The Integers
1
1.2 Well-Ordering
2
1.3 Induction
6
Exercises
7
Chapter 2
Divisibility
10
2.1
Division
10
2.2 Greatest Common Divisors
22
2.3 The Equation aX
bY =
c
21
Exercises
30
Chapter *3
Prime Numbers
33
3.1
Primes
33
3.2 A Sieve Method
39
3.3 Fermat Factorization
40
3.4 Some Unsolved Problems
41
Exercises
42
Chapter 4
Congruences
45
4. 1 Congruence
45
4.2
Inverses Modulo m
49
4.3 Fermat’s Little Theorem
53
4.4
Euler’s Theorem
55
4.5 A Historical View
58
4.6 Wilson’s Theorem
60
Exercises
62
Chapter 5
Multiplicative Functions
66
5.1
Three Special Functions
66
5.2
Perfect Numbers
71
5.3 Mobius Inversion
74
Exercises
79
Chapter 0
Solving Congruences
82
6. 1 The Congruence aX = b mod m
83
6.2 Systems of Linear Congruences
85
6.3 The Congruence
= a mod m
101
6.4 A General Theorem
111
Exercises
113
Chapter 7
Sums of Squares
119
7.1
Pythagorean Triples
123
7.2 Sums of Two Squares
128
7.3 Sums of Four Squares
134
Exercises
139
Chapter 8
Primitive Roots
143
Exercises
151
Chapter 9
Quadratic Reciprocity
153
9.1 The Legendre Symbol
153
9.2 The Quadratic Reciprocity Theorem
158
Exercises
175
Table of Squares
177
Table of Primes Less Than 10,000
178
Index
191
