Question 7
Let $m \gt 1$ be an integer. A sequence $a_{1}, a_{2}, a_{3}, \ldots$ is defined by $a_{1} = a_{2} = 1$, $a_{3} = 4$, and for all $n \geq 4$,
$$
a_{n} = m\left(a_{n-1} + a_{n-2}\right) - a_{n-3}.
$$
Determine all integers $m$ such that every term of the sequence is a square.
$$
a_{n} = m\left(a_{n-1} + a_{n-2}\right) - a_{n-3}.
$$
Determine all integers $m$ such that every term of the sequence is a square.