Question 183
Let $a_{1}, a_{2}, \ldots$ be a sequence of integers defined by $a_{1}=3$, $a_{2}=3$, and
$$
a_{n+2}=a_{n+1} a_{n}-a_{n+1}-a_{n}+2
$$
for all $n \geq 1$. Find the remainder when $a_{2020}$ is divided by $22$.
$$
a_{n+2}=a_{n+1} a_{n}-a_{n+1}-a_{n}+2
$$
for all $n \geq 1$. Find the remainder when $a_{2020}$ is divided by $22$.