Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton’s engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

Table of Contents

1 Preliminaries

2 Divisibility Theory in the Integers

3 Primes and Their Distribution

4 The Theory of Congruences

5 Fermat's Theorem

6 Number-Theoretic Functions

7 Euler's Generalization of Fermat's Theorem

8 Primitive Roots and Indices

9 The Quadratic Reciprocity Law

10 Introduction to Cryptography

11 Numbers of Special Form

12 Certain Nonlinear Diophantine Equations

13 Representation of Integers as Sums of Squares

14 Fibonacci Numbers

15 Continued Fractions

16 Some Modern Developments