Question 6
A sequence of integers $(a_n)$ determined by
$$
a_0 = 1,\ a_1 = -1 \quad \text{and} \quad a_n = 6a_{n-1} + 5a_{n-2} \quad \text{for all } n \ge 2.
$$
Show that $a_{2012} - 2010$ is divisible by $2011$.
$$
a_0 = 1,\ a_1 = -1 \quad \text{and} \quad a_n = 6a_{n-1} + 5a_{n-2} \quad \text{for all } n \ge 2.
$$
Show that $a_{2012} - 2010$ is divisible by $2011$.