The question has 3 parts:

My Attempt:

(a)Since the cyclic group generated by a is , I think it would follow that for distinct

but I don't know how to actually prove this. I appreciate any hints to get started.

(b)Though I'm not sure if it helps... but I think in general where . Is that correct?

(c)Is the gcd(a,b) required to be 1 (so that a and b are relatively prime)? If so I get

Is "h" equal to 1?