I want to prove $x^{p-1}+x^{p-2}+...+x+1$ irreducible over $\mathbb{Q}(\sqrt[p]{2})$ for $p$ prime. I have read somewhere it used the fact that $(p,p-1)=1$, but I don't understand. Can someone explain this?
2026-03-29 18:34:24.1774809264
Prove of irreducibility of polynomial over field extension
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