if g is an element of a group G and g has finite order, let's say n. then prove that the order of g^k is equal to (n/gcd(n,k)) i.e |g^k|= n/gcd(n,k)
my attempt: if n divides k then g^k=e. then the order of g^k is 1 and 1 = n/gcd(n,k) = n/n if n doesn't divide k then k= nr+s, where s<n and r,s are integers then g^k= g^nr g^s = g^s then I do not know what to do I am stuck here
