Abstract : Let $\Phi_n(x)=\sum_{k=0}^{\phi(n)}a(n,k)x^k$ denote the $n$-th cyclotomic polynomial. In this note, let $p < q < r$ be odd primes, where $q \not\equiv 1\pmod p$ and $r\equiv -2\pmod {pq}$, we construct an explicit $k$ such that $a(pqr,k)=-2$.
