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Dolly
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Let $m \in \mathbb Z, m>1$, then $\cos(2 \pi/m) \in \mathbb Q$ if and only if $m \in \{1,2,3,4,6\}$. [duplicate]
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Let $m \in \mathbb Z, m>1$, then $\cos(2 \pi/m) \in \mathbb Q$ if and only if $m \in \{1,2,3,4,6\}$.
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