Question 100
The sequence $\{x_n\}$ is defined by $x_1 = a$, $x_2 = b$ and $x_n = 2008x_{n-1} - x_{n-2}$ for all $n \ge 2$. Prove that there are positive integers $a$ and $b$ such that for all $n \ge 1$ the expression $1 + 2006x_nx_{n+1}$ is a perfect square. (Şahin Emrah).