Describe the set of all ordered pairs $(m, n)$ of positive integers such that $m^2 − mn + n^2$ is a perfect square.

Question

I'm stuck on this question. My attempt goes like this.

$m^2 - mn + n^2 - (m - n + k)^2$

$mn = 2km - 2kn + k^2$

$(m + 2k)(n - 2k) = 3k^2$

Any ideas on how to proceed? Any help is appreciated. Thanks!