Question 83
Let $x_1,x_2,x_3,\ldots$ be the sequence defined by
$$\begin{cases}x_1=4,\\x_{n+1}=x_1x_2\cdots x_n+5\quad(n\geq1).\end{cases}$$
(The first terms are $x_1=4$, $x_2=4+5=9$, $x_3=4\cdot9+5=41$, $\ldots$.) Find all pairs of positive integers $\{a,b\}$ such that $x_ax_b$ is a perfect square.
$$\begin{cases}x_1=4,\\x_{n+1}=x_1x_2\cdots x_n+5\quad(n\geq1).\end{cases}$$
(The first terms are $x_1=4$, $x_2=4+5=9$, $x_3=4\cdot9+5=41$, $\ldots$.) Find all pairs of positive integers $\{a,b\}$ such that $x_ax_b$ is a perfect square.