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Dec 3, 2015 at 8:36 comment added Johannes Trost +1 fro the explanation and also for the figures.
Aug 26, 2015 at 10:40 comment added Peter Mueller The discriminant of $\phi_n(x,\alpha)$, with respect to $x$, seems to be a polynomial in $\alpha$ with all coefficients of the same sign (or $0$). If one can prove that, this would be the missing piece.
Aug 26, 2015 at 9:20 history edited Peter Mueller CC BY-SA 3.0
another fix
Aug 26, 2015 at 8:51 history edited Peter Mueller CC BY-SA 3.0
simplified the partial proof, fixed small errors
Aug 25, 2015 at 19:19 history edited Peter Mueller CC BY-SA 3.0
added images which illustrate the argument
Aug 25, 2015 at 19:14 history edited Peter Mueller CC BY-SA 3.0
added images which illustrate the argument
Aug 25, 2015 at 15:22 history edited Peter Mueller CC BY-SA 3.0
added 585 characters in body
Aug 25, 2015 at 11:46 history answered Peter Mueller CC BY-SA 3.0