MathNet 2004 — Part 01 Question 91

Let $p(x)$ and $q(x)$ be polynomials with $m \geq 2$ non-zero coefficients. If $\frac{p(x)}{q(x)}$ is not a constant function, find the least possible number of the non-zero coefficients of the polynomial $f(u, v)=p(u) q(v)-p(v) q(u)$.