AUSTRIAN-POLISH 2002 Problem 5

Let $A$ be the set $\{2,7,11,13\}$ . A polynomial $f$ with integer coefficients possesses the following property: for each integer $n$ there exists $p \in A$ such that $p|f(n)$ . Prove that there exists $p \in A$ such that $p|f(n)$ for all integers $n$ .