I am looking for a counter-example for the following:
If $p(x)$ is an irreducible polynomial over $Z[x]$, then there is a polynomial in $Z[x], q(x)$, so that $p(q(x))$ is irreducible by Eisenstein's criterion.
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You could just take $g(x)=x$. The question asks for one such polynomial. – Jack's wasted life Jan 21 '16 at 14:32
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1I guess that is not what the question is asking for, but if you take $p(x)=l$ for a prime number $l$, this is an irreducible polynomial which doesn't change under precomposition and you cannot strictly speaking apply Eisenstein's criterion to it... – jorst Jan 21 '16 at 14:56
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That's not what I'm looking for. – Jan 21 '16 at 18:49