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Are there some necessary conditions on the coefficients of a monic, irreducible polynomial $\Phi$ over a local field?

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    The first comment is not quite right: try x. :)2011-12-20

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A corollary of Hensels lemma: If K is a field that is complete with respect to a non-archimedean absolute value, then for an irreducible polynomial $P=\sum{a_iX^i}$ of degree $n$ we have max($|a_i|$)=max($|a_0|$,$|a_n|$)

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    Corollary 4.7 in Chap$t$er 2 of Neukirch "Algebraic number theory".2011-12-20