Question 102
Let $m$ and $n$ be two integers and define $a_0 = m$, $a_1 = n$ and $a_{k+1} = 4a_k - 5a_{k-1}$ for $k \ge 1$. If $p \gt 5$ is a prime such that $p-1$ is divisible by $4$, then show that there are integers $m$ and $n$ such that $p$ does not divide $a_k$ for any $k \ge 0$.