Elementary Number Theory: Primes, Congruences, and Secrets

William Stein

The approach in this 165 page book tends to be more sophisticated than other books for the first number theory course, but it motivates much of the material with public key cryptography. It also uses Sage in order to deal with more realistic examples—such as RSA codes based on primes with more than 30 digits. Although published commercially by Springer, the publisher has granted access to a free pdf version that individuals can download, use, and print.