Prove that : $x^n+4$ is irreducible on $\mathbb{Z}[x]$ if only if $n\neq 4k$ with $k\in\mathbb{N}$.
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2$x^8+4$ is reducible: $x^8+4=(x^4-2x^2+2)(x^4+2x^2+2)$ but $8 \not =4^k$. – Ivan Loh Nov 29 '13 at 17:50
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Perhps you meant $4k$ rather than $4^k$? – Peter Košinár Nov 29 '13 at 19:16
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$4k$ is that true.I sorry all. – Hung Nguyen Dec 05 '13 at 10:01
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1http://math.stackexchange.com/questions/133581/when-is-xn-a-is-irreducible-over-f – Prahlad Vaidyanathan Dec 05 '13 at 10:30