Elementary Number Theory: Primes, Congruences, and Secrets

William Stein

Digital versions PDF
Latex source Yes
Exercises Yes
Answers and hints Yes
License Copyright held by Springer
  • Text for a first course in number theory following abstract algebra
  • The pdf version is free and can be printed but Springer reserves all rights for print distribution.
  • The LaTeX source is available on github.
  • Published version for $40 to $50 from various sellers
  • For more information and to download

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.

Table of Contents

  1. Prime Numbers
  2. Ring of Integers Mod n
  3. Public-key Cryptography
  4. Quadratic Reciprocity
  5. Continued Fractions
  6. Elliptic Curves