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In a post several years ago---

A sine product with (almost) integer values

a user observed that under some certain conditions,

$$ n \left( \prod_{k \in S_{n}} \sin \left( k \frac {\pi}{n} \right) \right)^{-2} $$

is (almost) an integer.

Another user offered a link to an (unnamed) paper by S. Galovich, but the link has since expired. Does anyone know of which of Galovich's papers may have contained theorem(s) pertaining to the above observation? (Galovich is now deceased.) Also, does anyone know of other similar products involving the sine function or any other trigonometric functions that might produce ``almost'' integer values? Thanks.

DDS
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  • I've looked for the document, and it think it should be this one: (products of sines and cosines, Steven Galovich, Math magazine, Vol 60, No 2, April 1987); https://www.tandfonline.com/doi/abs/10.1080/0025570X.1987.11977283 – Sudix Jun 24 '19 at 21:00
  • https://math.stackexchange.com/q/2777933 – user Jun 24 '19 at 23:27
  • @user Thank you for this link. – DDS Jun 25 '19 at 00:31
  • @Sudix Thank you. I look forward to obtaining the whole paper. – DDS Jun 25 '19 at 00:33

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