Question 172
The sequence $(a_n)$ is defined as follows: $a_0 = 1$, $a_1 = 1$, and
$$
a_{n+1} = 2(a_n - a_{n-1}),
$$
for all positive integers $n$. Determine, with proof, the remainder of $a_{2016}$ on division by $2017$.
$$
a_{n+1} = 2(a_n - a_{n-1}),
$$
for all positive integers $n$. Determine, with proof, the remainder of $a_{2016}$ on division by $2017$.