10. For what value of $x$ does the equation $\sin \frac{\pi}{1+x^{2}}$ $=0$ hold?
10. Let $1+x^{2}=\frac{1}{k}$, where $k$ is an integer, $k \neq 0$, then
$$
x= \pm \sqrt{\frac{1}{k}-1} .
$$

Only when $k=1$, $x$ is a real number, so $x=0$.