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Math Help - Sum of powers of unity root

  1. #1
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    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:
    <br />
\sum_{q \in S}\omega^q_n\notin Z <br />
    where \omega_n=e^{i\frac{2\pi}n}.
    Last edited by rodeo; August 17th 2008 at 05:47 PM.
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