Let $\mathbb{F}$ be a finite field, is it true that for any $n\ge 0$ there exists an irreductible polynomial $ P \in \mathbb{F}[X]$ of degree larger than $n$ ?
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For each finite field $\Bbb F$ and each number $n\geq 1$ there is an irreducible polynomial of degree $n$. – Wuestenfux Dec 04 '21 at 15:10
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Hint: a finite field cannot be algebraically closed – lhf Dec 04 '21 at 16:29
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@JoséCarlosSantos Yes, thank you. – Kieran McShane Dec 04 '21 at 17:24