Hi all, here is a little conjecture (I do have my proof but it could be interesting to see others' proofs), let's see how you do.

Say $\displaystyle n = pq$ with $\displaystyle p$ and $\displaystyle q$ primes ($\displaystyle n$ is a semiprime, thus).

Prove that there exists only two distinct solution pairs $\displaystyle (a, m)$ such that $\displaystyle m^2 - 4n = a^2$ with $\displaystyle m \in N$, $\displaystyle a \in N$.

Good luck !