Question at the end: Prove that the number of elements of $(\mathbb Z / n\mathbb Z)^\times$ is $\varphi(n)$ where $\varphi$ denotes the Euler function. I’ve demonstrated that it works for all n up to 12... Work showing n=1-12
It seems kinda obvious that not only does $\varphi(n)$ give the number of elements of $(\mathbb Z / n\mathbb Z)^\times$, but also the list of numbers are the same.
Question: I need a nudge in the right direction here. I can see that it works but I’m not sure how the remainders being equal to the relatively prime factors connects in a proof.