Question 95
Let $a \gt 1$ be a positive integer. The sequence $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ is defined by $a_{1} = 1$, $a_{2} = a$ and $a_{n+2} = a \cdot a_{n+1} - a_{n}$ for $n \geq 1$. Prove that the prime factors of its terms are infinitely many.