Question 169
Let $f(x) = ax^2 + bx + c$ be a polynomial with integer coefficients. For every integer $x$ $f(x)$ is divisible by $N$ where $N$ is a positive integer. Is it true that $N$ necessarily divides all the coefficients of $f(x)$ if
$$
\text{a) } N = 2016; \quad \text{b) } N = 2017?
$$
$$
\text{a) } N = 2016; \quad \text{b) } N = 2017?
$$