Let $n \in \Bbb{N}$ for which there exist two coprime numbers bigger than 2 dividing n. Show that for every x coprime to n we have $n|x^ {\phi(n)/2} − 1$. Conclude that there is no primitive root modulo n.
How does the fact the two coprime numbers bigger than 2 divide $n$ help? I tried using factorization and other theorems but I don't get anywhere. Besides, I have to prove that $x^{\phi(n)/2}\equiv1 \mod n$, but I could as well prove that $x^{\phi(n)}\equiv 1^2=1 \mod n$ so why is dividing $\phi(n)$ by 2 necessary? I could really use your help, any direction or hint is to what I might be overlooking.