RSA prove $a^{\varphi(n)/g} \equiv 1 \pmod{n}$
Hint: try to prove that $a^{phi(n)/g} \equiv 1 \pmod p$ for all $a$ satisfying $gcd(a, n) = 1$.

Metahint: $phi(n)/g = (p-1) \times (q-1)/g$; is $(q-1)/g$ an integer?