Question 197
The sequence $a = (a_0, a_1, a_2, \dots)$ is defined by $a_0 = 0$, $a_1 = 2$ and
$$
a_{n+2} = 2a_{n+1} + 41a_n \quad \text{for all } n \ge 0.
$$
Prove that $a_{2016}$ is divisible by $2017$.
$$
a_{n+2} = 2a_{n+1} + 41a_n \quad \text{for all } n \ge 0.
$$
Prove that $a_{2016}$ is divisible by $2017$.