# Math Help - Sum of powers of unity root

1. ## Sum of powers of unity root

Let $G_n(1)=\{q\in Z_n|(q,n)=1\}$ $S\subset G_n (1)$ (strict subset). Prove that:
$
\sum_{q \in S}\omega^q_n\notin Z
$

where $\omega_n=e^{i\frac{2\pi}n}.$