1. The problem statement, all variables and given/known data Let a belong to a group and |a| = m. If n is relatively prime to m, show that a can be written as the nth power of some element in the group. 2. Relevant equations We know : |a| = m gcd(m,n) = 1 We want to show : bn = a for some b in the group. 3. The attempt at a solution Okay, I didn't really know where to start with this one, but I'll give it a try. We know the gcd can be written as a linear combination, that is : gcd(m,n) = 1 = ms + nt for some integers s and t. Now : 1 = ms + nt a1 = ams + nt a = ams ant a = easant a = asant Here's where I get stuck. Any pointers?