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Nov 27, 2016 at 9:55 vote accept B. S.
Jun 15, 2015 at 18:53 comment added Michael Stoll @BogdanSimeonov Eisenstein works because the extension ${\mathbb Q}(\cos (2\pi/p))/{\mathbb Q}$ is totally ramified at $p$ (it is the maximal real subfield of the $p$th cyclotomic field).
Jun 15, 2015 at 14:30 comment added B. S. Thanks!It still remains a mystery why Eisenstein works here, I would love to see someone post a solution using it.
Jun 15, 2015 at 11:51 history edited Gabriel Dill CC BY-SA 3.0
inserted the forgotten i in the exponents...
Jun 15, 2015 at 9:13 history answered Gabriel Dill CC BY-SA 3.0