Characterization of modules of finite projective dimension over complete intersections

Let $M$ be a finitely generated module over a local complete intersection $R$ of characteristic $p>0$. The property that $M$ has finite projective dimension can be characterized by the vanishing of $\operatorname{ext}_R^i({}^{f^n} R,M)$ for some $i>0$ and for some $n>0$.