Elementary Theory of Numbers

Introduction

This superb text introduces number theory to readers with limited formal mathematical training. Intended for use in freshman- and sophomore-level courses in arts and science curricula, in teacher-training programs, and in enrichment programs for high-school students, it is filled with simple problems to stimulate readers' interest, challenge their abilities and increase mathematical strength.

Contents

I. Introduction

II. The Euclidean Algorithm and Its Consequences

III. Congruences

IV. The Powers of an Integer Modulo m

V. Continued Fractions

VI. The Gaussian Integers

VII. Diophantine Equations

Requiring only a sound background in high-school mathematics, this work offers the student an excellent introduction to a branch of mathematics that has been a strong influence in the development of higher pure mathematics, both in stimulating the creation of powerful general methods in the course of solving special problems (such as Fermat conjecture and the prime number theorem) and as a source of ideas and inspiration comparable to geometry and the mathematics of physical phenomena.