1) Show that ifpis an odd prime andris a primitive root ofp, then $\displaystyle ind_{r}$(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.)