nonnegative m, n

\(\frac{1}{m} + \frac{1}{n} = \frac{2^2}{(mn^2)}\) whereby m and n are positive integers and \(m \neq 0\) and \(n \neq 0\).

So when m and n are positive then \(n(m + n) = 4\).

Distribute \(n^2 + nm = 4\).

There is only one solution: m = 3 and n = 1.

thanks