Finding the common integer solutions to $a + b = c \cdot d$ and $a \cdot b = c + d$ I find nice that $$ 1+5=2 \cdot 3 \qquad 1 \cdot 5=2 + 3 .$$

Do you know if there are other integer solutions to
  $$ a+b=c \cdot d \quad \text{ and } \quad  a \cdot b=c+d$$
  besides the trivial solutions $a=b=c=d=0$ and $a=b=c=d=2$?


I found that, through solving the equations, we will have following (if a>b):
$$a=\frac{cd+\sqrt{c^2d^2-4(c+d)}}{2}$$
and
$$b=\frac{cd-\sqrt{c^2d^2-4(c+d)}}{2}$$
I think it will be useful for you to find all of the solutions.
Only you should find the solutions for: 
$$c^2d^2-4(c+d)=m^2$$
where $m$ is any positive integer. 
