1) Show that if p is an odd prime and r is a primitive root of p, then (p-1) = (p-1)/2
2) Prove that there are infinitely many primes of the form 8k+1.
(Hint: Assume that p1, p2, ..., pn are the only primes of this form. Let Q = (2p1, p2....pn)^k + 1. Show that Q must have an odd prime factor different than p1, p2, ...., pn, and must be of the form 8k + 1.)