Generalized Giuga conjecture for finite commutative rings

Let $R$ be a finite commutative unital ring, and let $|R|$ denote its cardinality. Generalized Giuga conjecture.

$$\sum_{r\in R}r^{|R|-1}=-1$$

if and only if $R$ is a field. This generalizes the classical Giuga conjecture, which characterizes prime integers through the corresponding power sum modulo $n$. The source proposes this statement as a generalization and gives no resolution; it remains open.