Small exponents and the RSA problem
Can you please give me some direction for such proof? 


You're looking for a proof that the RSA problem is hard?  No such proof is known (even in the specific case of $e=3$).  Furthermore, there is no known reduction to a 'more fundamental' problem, such as factorization or discrete log.

The closest we can get is a proof that if you can find the 'decryption exponent', that is, the value $d$ such that $y^d \equiv x \pmod N$, you can factor $N$ (and using the value $d$ is how the holder of the RSA private key recovers $x$ in practice).  However, this does not show that there isn't another way (that's easier than factoring) to recover $x$.

The only 'proof' we have that the RSA problem is hard is 'lots of smart people have looked for a way to solve it, and they haven't found one'