# Sum of powers of unity root

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• August 15th 2008, 10:07 AM
rodeo
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 $\omega_n=e^{i\frac{2\pi}n}.$