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i found this relation whilst trying to evaluate the norm (over $\mathbb{Q}$) of $1-\zeta$ for $\zeta$ a primitive $p$-th root of unity ($p$ supposed prime) $$ \prod_{k=1}^{p-1} \sin(\frac{\pi k}{p}) = \frac{p}{2^{p-1}} $$ as yet i have no means of proving it. any suggestions?


marked as duplicate by Daniel Fischer Mar 8 '15 at 10:25

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  • $\begingroup$ thanks, that looks very useful $\endgroup$ – David Holden Nov 1 '14 at 15:58
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    $\begingroup$ While information at this link may answer the question, currently this is not an answer. Please consider including the essential parts of the answer here, and provide the link for reference. $\endgroup$ – user642796 Nov 2 '14 at 4:14

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