Here's a question I would like hints for:
The sequence ${x_n}$ is defined by $x_{n+2}=6x_{n+1}-9x_{n}$ for $n \geq 0$ where $x_0=3$ and $x_1=18$. What is the smallest $k$ such that $x_k$ is divisible by $2013$?
I'm not sure how to start this one. I'd like hints rather than a full solution. Also, is there some sort of general technique for approaching such problems?