Question 39
Determine the finite commutative rings $A$ with at least four elements, with the property that for any choice of a proper subset $S$ of $A^*$ with at least two elements, the equality
$$
\sum_{x \in S} x = \prod_{x \in A^* \setminus S} x
$$
holds.
$$
\sum_{x \in S} x = \prod_{x \in A^* \setminus S} x
$$
holds.