Hey everyone I was wondering if anybody could help me with this problem.
Let G = <x> where x has order n and let r denote a positive integer. Prove that
generates G if and only if gcd(r,n) = 1, i.e. r and n are coprime.
I guess I am trying to prove the statement
.
When I try to do this however I just get a strange result... I would appreciate any guidance with this to see where I have gone wrong or what I can do to solve it.
Proof (<=)
such that
So
since |x| = n.
Also
since |x| = n.
Hence
giving
which of course means
.
Is this right, have I done something wrong?? Any help would be appreciated.