Question 85
Find all positive integers $n$, $n \ge 3$, for which there exists a set $M$, whose elements are $n$ distinct, nonzero vectors, with equal lengths, such that $\sum_{\vec{u} \in M} \vec{u} = \vec{0}$, but for any $\vec{v}, \vec{w} \in M$, we have $\vec{v} + \vec{w} \ne \vec{0}$.