Solve the following equation:

$$
\frac{x^{2}}{(m+n)^{2}}-\frac{4 m n}{(m+n)^{2}} x-(m-n)^{2}=0
$$
Our equation can also be written as:

$$
x^{2}-4 m n x-\left(m^{2}-n^{2}\right)^{2}=0
$$

or

$$
\begin{aligned}
x^{2}-4 m n x+4 m^{2} n^{2} & =\left(m^{2}-n^{2}\right)^{2}+4 m^{2} n^{2} \\
(x-2 m n)^{2} & =\left(m^{2}+n^{2}\right)^{2}
\end{aligned}
$$

from which

$$
x_{1}=m^{2}+n^{2}+2 m n=(m+n)^{2}
$$

and

$$
x_{2}=-m^{2}-n^{2}+2 m n=-(m-n)^{2}
$$

(Sichermann Frigyes, Kassa.)

Number of solutions: 19.