Australian AMC 2016 - Senior Question 27

Let $a,b,c,m,n$ be integers such that $m<n$ and define the quadratic function $f(x)=ax^2+bx+c$ where $x$ is real. Then $f(x)$ has a graph that contains the points $(m,0)$ and $(n,2016^2)$. How many values of $n-m$ are possible?