Elementary Number Theory

Traditionally, elementary number theory is a branch of number theory dealing with the integers, but without use of techniques from other mathematical fields. In this concise and elegant book, the author has sought to pare away all material that might be considered extraneous to a three-hour-per-week, twelve-week semester course in elementary number theory. The author presents in natural sequence the basic ideas and results of elementary number theory, laying a strong foundation for later studies in algebraic number theory and analytic number theory. The only background knowledge required of the reader is of some simple properties of the system of integers. Elementary Number Theory begins with a few preliminaries on induction principles, followed by a quick review of division algorithms. Then in the second chapter, the author touches upon the usage of divisors, the greatest (or least) common divisor (multiple), the Euclidean algorithm, and linear indeterminate equations. This foundation supports discussions in the subsequent chapters concerning: prime numbers; congruences; congruent equations; and, finally, three additional topics (comprising cryptography, Diophantine equations and Gaussian integers). Each chapter concludes with exercises that both illustrate the theory and provide practice in the techniques. Answers to even-numbered problems are given at the end of the book.