Theory of Numbers

the long version

Theory of Numbers is a carefully written textbook for an elementary number theory course with minimal prerequisites. It begins with the classical theory of divisibility, primes, and modular arithmetic; and ends with computational topics of factorization, pseudoprimes, and primality testing. Ideal for self-study or for a one-semester course, the relatively small, measured contents include numerous exercises strategically dispersed throughout the text in order to retain theoretical context and reinforce understanding. As an extended workout, every chapter concludes with a partially guided project touching on a wide range of problems, from the old sums-of-squares theorems to the more recent cryptographical protocols.