X^(p-1)+...+X+1/Irreduzibel/Aufgabe

Es sei ${}p$ eine Primzahl. Betrachte das Polynom

{}P=X^{p-1}+X^{p-2}+\cdots +X^{2}+X+1\,.

Zeige, dass ${}P$ irreduzibel

in

{}\mathbb {Q} [X]

ist.

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