I have one more question:
Let $n=pq$ with $p,q \in \mathbb{P}$, then we have $p-1 \mid n-1$ and $q-1 \mid n-1$. I don't understand the reason the author tells me: "because there are multiplicative groups of integers modulo $p$ and modulo $q$." Is there any way to proof the existence of the prime integers?
Any help is appreciated.