No. of solutions of $m^4 = 9n^2 + 72$ where $m$ and $n$ are integers

Question

No. of solutions of $m^4 = 9n^2 + 72$ where $m$ and $n$ are integers

My approach:

I figured out that $m$ has to be a multiple of $3$ , so from here I am able to get $4$ solutions $(3,1)$, $(3,-1)$, $(-3,1)$ and $(-3,-1)$.

How can I check for other possible solutions?

Answer 1

Assuming it should be $m^4 = 9n^2 + 72$ based on what you wrote.

Hint: $$m^4 - 9n^2 = (m^2 - 3n)(m^2 + 3n)$$