Consider the polynomial $$ f(x) = x^{p} + x^{p-1} + \ldots + x + 1 $$ over $\mathbb{Q}$, where $p$ is a prime number. Is it true that $f$ is irreducible?
2026-04-02 15:58:42.1775145522
Irreducible polynomial of prime degree
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Yes, if $p=2$. No, otherwise: $-1$ is a root then.