Question 6
Let $a$, $b$ be relatively prime positive integers and let $a_n$ and $b_n$ be integer sequences satisfying $(a + b\sqrt{2})^{2n} = a_n + b_n\sqrt{2}$. Find all primes $p$ such that there is a positive integer $n$ less than or equal to $p$ satisfying $b_n \equiv 0 \pmod{p}$.