Let $f(x) = x^n + a_{n-1} x^{n-1} + \cdots + a_0$ be a polynomial with integer coefficients and whose degree is at least 2. Suppose each $a_i$ ($0 \leq i \leq n-1$) is of the form
$$a_i = \pm \frac{17!}{r!(17-r)!}$$
with $1 \leq r \leq 16$. Show that $f(m)$ is not equal to zero for any integer $m$.