Question 6Let $a,b$ be odd natural numbers such that $a$ divides $b^2+2$ and $b$ divides $a^2+2$. Prove that $a$ and $b$ are terms of the natural-number sequence $(v_n)$ defined by $v_1=v_2=1$ and $v_n=4v_{n-1}-v_{n-2}$ for every $n\ge3$.