Square-free values of f(p), f cubic

Let \({f \in \mathbb{Z}x]}\) , \({\deg f =3}\) . Assume that f does not have repeated roots. Assume as well that, for every prime q, \({f(x)\not\equiv 0}\) mod q ² has at least one solution in \({(\mathbb{Z}/q^2 \mathbb{Z})^*}\) . Then, under these two necessary conditions, there are infinitely many primes p such that f(p) is square-free.