Solution 15. Every meromorphic function, $f$, is holomorphic with poles at some sequence $p_1, p_2, \ldots$ Then there is an entire function with zeros precisely at the $p_j$ with desired multiplicity. Call this function $g$. Then $f g$ has no poles and is holomorphic except possibly at the $p_j$, but since there are no poles at the $p_j$, we see that we have an entire function, say $h$. Then $f=g / h$. For the second part of the problem construct two entire functions and take their quotient.