Question 90
Let $p$ and $q$ be prime numbers and let the sequence $\{a_n\}_{n=1}^{\infty}$ be defined by:
$$
a_0 = 0, a_1 = 1 \text{ and } a_{n+2} = pa_{n+1} - qa_n
$$
for $n \ge 0$. Find $p$ and $q$ if it is known that $a_{3k} = -3$ for some integer $k$.
$$
a_0 = 0, a_1 = 1 \text{ and } a_{n+2} = pa_{n+1} - qa_n
$$
for $n \ge 0$. Find $p$ and $q$ if it is known that $a_{3k} = -3$ for some integer $k$.