Elementary Theory of Numbers

Description

Superb introduction for readers with limited formal mathematical training. Topics include Euclidean algorithm and its consequences, congruences, powers of an integer modulo m, continued fractions, Gaussian integers, Diophantine equations, more. Carefully selected problems included throughout, with answers. Only high school math needed. Bibliography.;Cover; Title Page; Copyright Page; Preface; Contents; Chapter 1. Introduction; 1-1 What is number theory?; 1-2 Foundations; 1-3 Proofs by induction; 1-4 Indirect proofs; 1-5 Radix representation; Chapter 2. The Euclidean Algorithm and its Consequences; 2-1 Divisibility; 2-2 The Euclidean algorithm and greatest common divisor; 2-3 The unique factorization theorem; 2-4 The linear Diophantine equation; 2-5 The least common multiple; Chapter 3. Congruences; 3-1 Introduction; 3-2 Elementary properties of congruences; 3-3 Residue classes and arithmetic (mod m).