Question 28
Let $(K, +, \cdot)$ be a finite field with at least four elements. Prove that the set $K^*$ can be partitioned into two nonempty subsets $A$ and $B$, such that
$$
\sum_{x \in A} x = \prod_{y \in B} y.
$$
$$
\sum_{x \in A} x = \prod_{y \in B} y.
$$