# Random Diophantine Equation

Find the number of positive integers $n$ such that there exists an integer $m \neq \frac{n}{2}$ such that $\frac{n^3-2m^3}{6m}$ is a perfect square.


Details and Assumptions:

• All perfect squares are integers. For example, $8^2, 4^2,$ etc. are perfect squares, but $\left( \frac{2}{3} \right) ^2$ isn't.
×