Question 63
Let $n$ be a positive integer. Find all positive integers $m$, for which there exists a polynomial $f(x) = a_{0} + a_{1} x + \cdots + a_{n} x^{n} \in \mathbb{Z}[x],\ a_{n} \neq 0$, such that $\gcd(a_{0}, a_{1}, \ldots, a_{n}, m) = 1$ and $f(k)$ divides $m$ for any integer $k$.