Question 153
Let $(K,+, \cdot)$ be a finite field with at least four elements. Show that the set $K^{*}$ can be partitioned into two nonempty subsets $A$ and $B$ such that
$$
\sum_{x \in A} x=\prod_{y \in B} y
$$
$$
\sum_{x \in A} x=\prod_{y \in B} y
$$