Question 9
Suppose $\{a_n\}$ is a sequence in which all the terms are integers, and $a_2$ is odd. For any natural number $n$, $n(a_{n+1} - a_n + 3) = a_{n+1} + a_n + 3$. Furthermore, $a_{2009}$ is divisible by $2010$. Find the smallest integer $n$, $n \ge 2$, such that $a_n$ is divisible by $2010$.