Question 8
Find the number of positive integers $n$ less than $2017$ such that $$
\begin{aligned} &1 + n + \frac{n^2}{2!} + \frac{n^3}{3!} + \frac{n^4}{4!} \\ &{}+ \frac{n^5}{5!} + \frac{n^6}{6!} \end{aligned}
$$ is an integer.
\begin{aligned} &1 + n + \frac{n^2}{2!} + \frac{n^3}{3!} + \frac{n^4}{4!} \\ &{}+ \frac{n^5}{5!} + \frac{n^6}{6!} \end{aligned}
$$ is an integer.