SE-SKOLORNAS 1973 Problem 5

$f(x)$ is a polynomial of degree $2n$ . Show that all polynomials $p(x)$ , $q(x)$ of degree at most $n$ such that $f(x)q(x)-p(x)$ has the form $$\sum\limits_{2n<k\leq 3n} (a^k + x^k)$$ have the same $p(x)/q(x)$ .