We discussed the extended euclidean algorithm, and Example 6.19 on how to solve linear integer equation. We then went on to dicuss perfect numbers (Exercise 6.40), and the way to generate the even ones using Mersenne primes. It is not known whether there are any odd ones.
Some (not all) of this material is useful for cryptography (see e.g. the RSA Algorithm), but was discovered way before when people had no practical use in mind.