Elementary Number Theory

Presents a self-contained introduction to Number Theory, requiring a background knowledge only of some simple properties of the system of integers. This book features a few preliminaries on induction principles, followed by a quick review of division algorithm.

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This new volume presents a self-contained introduction to Number Theory, requiring a background knowledge only of some simple properties of the system of integers. The book begins with a few preliminaries on induction principles, followed by a quick review of division algorithm. The substance of the book starts in the second chapter, where, using divisors, the greatest (least) common divisor (multiple), the Euclidean algorithm, and linear indeterminate equation are discussed. This lays the foundation for the subsequent chapters dealing with: prime numbers; congruences; congruent equations; and, finally, three additional topics (comprising cryptography, Diophantine equations and Gaussian integers). At the end of each chapter are selected exercises to illustrate the theory and provide practice in the techniques. Answers to all even-numbered problems are given at the end of the book.