14. Let $f(x, y)$ be a bivariate polynomial, and satisfy the following conditions:
(1) $f(1,2)=2$; (2) $y f(x, f(x, y))=x f(f(x, y), y)=(f(x, y))^{2}$, determine all such $f(x, y)$.
14. From condition (2), we know that $x$ and $y$ are factors of $f(x, y)$, so let $f(x, y) = x y g(x, y)$, where $g(x, y)$ is also a bivariate polynomial. Substituting into condition (2) and simplifying, we get $g(x, y) = g(x, x y g(x, y)) = g(x y g(x, y), y)$. By comparing degrees, we know that $g(x, y)$ contains neither $x$ nor $y$, i.e., $g(x, y)=$ constant. Furthermore, from condition (1), we get $f(x, y) = x y$.