15 December 2022 0 1K Report

For $q\in \mathbb{N}$, $k,r\in \mathbb{Z}$ such that $k\ne rq$. Let $\zeta_q$ be the $q$-th root of unity then

\begin{equation}

\sum_{i=0}^{q-1} \zeta_q^{k\cdot i}=0.

\end{equation}.

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