Question 78
Let $\left(a_{n}\right)_{n \geq 0}$ be a sequence of positive integers such that $a_{n}^{2}$ divides $a_{n-1} a_{n+1}$, for all $n \geq 1$. Prove that if there exists an integer $k \geq 2$ such that $a_{k}$ and $a_{1}$ are relatively prime, then $a_{1}$ divides $a_{0}$.