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May 20, 2014 at 1:10 comment added GH from MO @Michael: I could not show independence of $s$, so I updated my writeup accordingly. Fortunately, David Speyer came up with an approach that is more to the point.
May 20, 2014 at 1:09 history edited GH from MO CC BY-SA 3.0
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May 19, 2014 at 20:44 comment added GH from MO @Michael: I am thinking about this. At the moment the argument only gives that each irreducible factor of $f_{n,a}$ has a $p$-power degree.
May 19, 2014 at 20:12 history edited GH from MO CC BY-SA 3.0
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May 19, 2014 at 20:06 history edited GH from MO CC BY-SA 3.0
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May 19, 2014 at 19:59 history edited GH from MO CC BY-SA 3.0
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May 19, 2014 at 18:25 history answered GH from MO CC BY-SA 3.0