Tuesday, 15 November 2016

abstract algebra - Does there always exist an irreducible polynomial of degree $d$ over $mathbb{Z}/pmathbb{Z}$?

Let $p$ be a prime and let $d$ be a positive integer. Does there always exist an irreducible (i.e. unfactorable) polynomial of degree $d$ over $\mathbb{Z}/p\mathbb{Z}$?

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