Let a be in a group G with |a| = m. If n is relatively prime to m, show that a = b^n for some b in G.

My Proof so far:

Now the order of a is m, so I have a^m = e, the identity. n is relatively prime to m, so I have ng + r = m for some integers g and r, with m > r > n.

umm... what now?