Let $N = pq$, $p$ and $q$ are prime. Define $\varphi(N)$ as an Euler's function, $e$ as a prime divisor of $\varphi(N)$ and numbers $\frac{p-1}{2}$, $\frac{q-1}{2}$ are coprime. I'm trying to proof that the problem of calculating the roots of degree $e$ modulo $N$ is equivalent in complexity to factorizing the number $N$.
I'm trying to make an equivalence between this problem and the problem of discrete logarithms in proper subgroups of order $\frac{p-1}{2}$, $\frac{q-1}{2}$, but have no results.
Do anybody have some ideas to proof that?