Prove that no $n,m, 0Prove or disprove the claim that there are integers $n,m, 0<n<m$ such that $m^2 +mn+n^2$
is a perfect square.

Hint $\rm\ \ A^2 + AB+ B^2 = (a^2+ab+b^2)^2\ $ for $\rm\ A = a^2-b^2,\,\ B = b^2 + 2ab$
This arises from the norm-multiplicativity $\rm\ N(\alpha^2) = (N(\alpha))^2\ $ for $\alpha$ an Eisenstein integer.
