Elements of Number Theory

Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.

Table of Contents

1 Natural numbers and integers

2 The Euclidean algorithm

3 Congruence arithmetic

4 The RSA cryptosystem

5 The Pell equation

6 The Gaussian integers

7 Quadratic integers

8 The four square theorem

9 Quadratic reciprocity

10 Rings

11 Ideals

12 Prime ideals