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Jul 31, 2018 at 17:56 comment added Peter Mueller @user221330 It was straightforward, because by separability of $t^{p^m}-t$, the question simply was when $\mathfrak p$ divides this polynomial, which in turn is equivalent to each root of $\mathfrak p$ dividing it.
Jul 31, 2018 at 17:36 comment added user221330 Thank you! Can I ask, what made you think of this solution? Was it incredibly obvious, or was there something that influenced your thinking?
Jul 31, 2018 at 17:31 vote accept user221330
Jul 31, 2018 at 17:13 history answered Peter Mueller CC BY-SA 4.0