Let $q,p$ prime numbers and $n=pq$. Let $r$ random from $Z^{*}_n$ and $e$ random element which is not contained in $\varphi(n)$. all values except $p$ and $q$ are known.
Let
$f_1(m) = m^e \text{ mod } n$
$f_0(m) = rm^e \text{ mod } n$
Assuming RSA problem is hard in $Z^{*}_n$ show that it is not possible to find $x,y$ such as $f_1(x)=f_0(y)$.
I know that I need to use reduction to the RSA problem, but I'm not quite sure how?
Note that $$f_1(x)=f_0(y) \iff x^e\equiv ry^e\pmod n\iff (xy^{-1})^e\equiv r\pmod n.$$ As inverting is easy in $\Bbb Z_n^\times$, finding such $x,y$ allows us to decrypt $r$, which is assumed hard for random $r$.