Find all integers $m,\ n$ such that $m^2+4n$ and $n^2+4m$ are both squares. 
Find all integers $m,\ n$ such that both $m^2+4n$ and $n^2+4m$ are perfect squares.

I cannot solve this, except the cases when $m=n$.

Hint : There is an useful technique dealing with some problems including squares. Assume $m \ge n$ and bound $m^2+4n$.
