As the title reads: In a cyclic group with $n$ elements, how many elements $x$ have the following property: $x^n=1$ ? where $1$ is the identity
I tried searching for an answer to this in my book and here, but I couldn't find a direct answer, so I apologize if this has been answered before in another post.
I feel like there's a theorem for this, I just can't seem to find it. I'm thinking the answer has to do with the number of generators, since the generators guarantee that we find the identity, so multiplying a generator element n times should give the identity, or am I completely off track?