I am trying to solve the Diophantine equation
$$4 k + m^2 = n^2$$
This looks very simple, but I stuck with this. I have represented this in terms of integers, but again no success:
$$k_2 n_2^2 m_1^2 + 4 k_1 n_2^2 m_2^2= k_2 n_1^2 m_2^2$$
I am trying to find such $k$ and $m$ that
$$4k+m^2$$ is square of rational number.
EDITED 2: The problem I am working on is finding of general solution for this equation.