Question 151
Let $P$ be a polynomial with real coefficients and such that for any positive integer $n$ the number $P(n)$ is an integer. There exist distinct prime integers $p_1, p_2, \dots, p_k$ such that for any positive integer $n$ the number $P(n)$ is divisible by at least one of $p_1, \dots, p_k$. Prove that there exists $i$ such that $p_i$ is a divisor of $P(n)$ for all integers $n$.