Contents

Preface	xiii
Programs by Type	vi
Programs by Section	viii
Warning	ix
Laboratories	1
1     GCDs & The Euclidean Algorithm       1
2     Factorization and Prime Numbers       7
3     Congruences       11
4     Sums of Two Squares       13
5     Solutions of Congruences & Binomial Coefficients       17
6     Linear Congruences & The Chinese Remainder Theorem       21
7     Powering Algorithms & Primality Testing       25
8     Factoring Strategies       29
9     RSA Public Key Cryptography       35
10     Hensel's Lemma       43
11     Power Residues & Primitive Roots       45
12     Indices --- The Discrete Logarithm       49
13     Proving Primality       55
14     Square Roots Modulo p       59
15     Quadratic Residues       61
16     Binary Quadratic Forms       65
17     Arithmetic Functions       69
Reference Guide to Turbo Pascal Programs	73