1. The problem statement, all variables and given/known data Let a be a generator of [tex]F_q[/tex] Prove that [tex]a^i[/tex] is a generator if & only if [tex]i[/tex] and [tex]q-1[/tex] are relatively prime. 2. Relevant equations a is a generator of [tex]F_q[/tex] means that a^(q-1) = 1 and [tex]a^i[/tex] cannot be 1 for all i not q-1. relatively prime means that [tex]gcd(i,q-1)[/tex]=1 fermats theorem says that: a^(p-1) = 1 (mod p ) where p is prime 3. The attempt at a solution => Suppose that [tex]a^i[/tex] is a generator of [tex]F_q[/tex]. then a^(i(q-1)) =1 (mod q) so by fermats theorem, gcd(i, q-1) = 1??? How does that sound?