Question 183
The sequence
$$
5, 9, 49, 2209, \ldots
$$
is defined by $a_{1} = 5$ and $a_{n} = a_{1} a_{2} \cdots a_{n-1} + 4$ for $n \gt 1$. Prove that $a_{n}$ is a perfect square for $n \geq 2$.
$$
5, 9, 49, 2209, \ldots
$$
is defined by $a_{1} = 5$ and $a_{n} = a_{1} a_{2} \cdots a_{n-1} + 4$ for $n \gt 1$. Prove that $a_{n}$ is a perfect square for $n \geq 2$.