We discussed the Chinese remainder theorem, and some examples, including Problem 7.35, where not all the n_{i} are relatively prime.

We also discussed how to solve such systems in an ad-hoc way, without using the formula given by the proof of the CRT.

We then went on to talk about multiplicative orders of elements, and proved Fermat's little Theorem (Theorem 7.36), as well as Lemma 7.43 on elements of order 2. These are not going to be explicitly covered in the test.

The last part of Chapter 7 in the book has more on this, with e.g. a proof that for p a prime, (p - 1)! ≡ -1 mod p (Theorem 7.44). Try to think about how you would prove this yourself before looking.