List questions from irreducible-polynomials

Published on 30 Nov 2017 - 21:26

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Writing a polynomial as a product of irreducible polynomials over another field

Published on 01 Dec 2017 - 8:45

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Irreducible polynomials $p(x),~q(x)\in \mathbb{Z}_2[x]$ such that $(x^3+1)p(x)+xq(x)=p(x)q(x).$

Published on 01 Dec 2017 - 15:46

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Prove that $x^6 + 24x - 20$ is irreducible over $\mathbb{Q}$

Published on 02 Dec 2017 - 20:54

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Prove that $x^5 + 4x^4 + 2x^3 + x^2 + 4x + 54$ is irreducible over $\mathbb{Z} / 7\mathbb{Z}$

Published on 02 Dec 2017 - 21:43

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Is $1+X^2$ irreducible in $\mathbb{Z}_3$?

Published on 02 Dec 2017 - 23:46

86

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Prove that $1+x+x^2+x^3+x^4+x^5+x^6$ is irreducible in Q[X]

Published on 04 Dec 2017 - 4:58

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Construction of finite fields

Published on 04 Dec 2017 - 22:37

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Simple extension is splitting field of $f=X^p-X+a \in K[X]$ with $char(K)=p$

Published on 23 Feb 2026 - 15:36

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Irreducibility of a polynomial over certain finite fields

Published on 06 Dec 2017 - 5:58

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Irreducible polynomial over $\mathbb{Q}(\sqrt[3]{2})$

Published on 06 Dec 2017 - 23:52

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Are irreducible polynomials square free?

Published on 31 Mar 2026 - 16:17

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Proving irreducibility of a polynomial

Published on 08 Dec 2017 - 2:24

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How to show this polynomial is irreducible?

Published on 08 Dec 2017 - 17:26

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irreducibility criteria over function fields

Published on 09 Dec 2017 - 17:10

List Question

Proving irreducible over $\mathbb{R}[x]$?

Writing a polynomial as a product of irreducible polynomials over another field

Irreducible polynomials $p(x),~q(x)\in \mathbb{Z}_2[x]$ such that $(x^3+1)p(x)+xq(x)=p(x)q(x).$

Prove that $x^6 + 24x - 20$ is irreducible over $\mathbb{Q}$

Prove that $x^5 + 4x^4 + 2x^3 + x^2 + 4x + 54$ is irreducible over $\mathbb{Z} / 7\mathbb{Z}$

Is $1+X^2$ irreducible in $\mathbb{Z}_3$?

Prove that $1+x+x^2+x^3+x^4+x^5+x^6$ is irreducible in Q[X]

Construction of finite fields

Simple extension is splitting field of $f=X^p-X+a \in K[X]$ with $char(K)=p$

Irreducibility of a polynomial over certain finite fields

Irreducible polynomial over $\mathbb{Q}(\sqrt[3]{2})$

Are irreducible polynomials square free?

Proving irreducibility of a polynomial

How to show this polynomial is irreducible?

irreducibility criteria over function fields

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