Question 19
A sequence $(a_n)$, $n \in \mathbb{N}$ is defined as
$$
a_1 = 1,\ a_2 = 2,\ a_3 = 3 \text{ and } a_n = \frac{a_{n-1} a_{n-2} + 7}{a_{n-3}}, \text{ for } n \ge 4.
$$
Prove that all terms of this sequence are integers.
$$
a_1 = 1,\ a_2 = 2,\ a_3 = 3 \text{ and } a_n = \frac{a_{n-1} a_{n-2} + 7}{a_{n-3}}, \text{ for } n \ge 4.
$$
Prove that all terms of this sequence are integers.