  Let $n$ be an even positive integer with at most three distinct prime factors
and let $\ze_n$ be a primitive $n$-th root of unity. In this study, we made an
attempt to find the lowest-degree $0,1$-polynomial $f(x) \in \Q[x]$ having at
least three terms such that $f(\ze_n)$ is a minimal vanishing sum of the $n$-th
roots of unity.
