26. Find the function $f$, defined on the set of all real numbers, if it is known that $f^{2}(x+y)=f^{2}(x)+f^{2}(y)$ for any $x$ and $y$.
76.26. Let's denote $f^{2}(x)$ by $g(x)$. Let $x$ and $y$ be arbitrary numbers, and $a=y-x$. Then $g(y)=g(x)+g(a)$ and also $g(x)=g(y-a)=g(y)+g(-a)$. Since $g(a) \geqslant 0, g(-a) \geqslant 0$, we get that $g(y) \geqslant g(x) \geqslant g(y)$. Therefore, $g$ is a constant, and obviously, it is zero. Thus, $g(x)=0$ and $f(x)=0$.