Question 126
Determine, with proof, whether there is a function $f(x, y)$ of two positive integers, taking positive integer values, such that
- For each fixed $x$, $f(x, y)$ is a polynomial function of $y$;
- For each fixed $y$, $f(x, y)$ is a polynomial function of $x$;
- However, $f(x, y)$ does not equal any polynomial function of $x$ and $y$.
- For each fixed $x$, $f(x, y)$ is a polynomial function of $y$;
- For each fixed $y$, $f(x, y)$ is a polynomial function of $x$;
- However, $f(x, y)$ does not equal any polynomial function of $x$ and $y$.