The proof of security of RSA I'm familiar with is if you could compute $$(p-1)(q-1),$$ then you could compute $p$ and $q$ from $$p+q=pq-(p-1)(q-1)-1$$ and $pq=n$.
A question I have is: is it clear under reasonable assumptions on $p,q$ that being able to decrypt $M^e$ implies you can calculate $(p-1)(q-1)$?