List questions from irreducible-polynomials

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Primitive polynomial vs irreducible polynomial for construction field $GF(2)[x]/\langle p(x)\rangle$

Published on 01 Apr 2026 - 20:02

1.2k

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Proof check: Irreducibility of $xy-1$

Published on 16 Aug 2017 - 5:08

30

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The splitting extention above Z_ (p)

Published on 17 Aug 2017 - 12:49

223

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Polynomial $x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1$ is reducible over $\mathbb{Q}$?

Published on 17 Aug 2017 - 17:02

137

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How to prove this polynomial is irreducible over $\mathbb{Q}$

Published on 22 Aug 2017 - 12:06

999

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Irreducible polynomial of degree $2$ over a finite field of characteristic $2$

Published on 23 Aug 2017 - 4:04

222

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A root of irreducible polynomial in field extension (proof)

Published on 25 Aug 2017 - 10:48

87

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Sufficient Conditions for (Ir)reducibility

Published on 07 Apr 2026 - 22:49

107

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Factorization and GCD for Rijndael's finite field

Published on 06 Apr 2026 - 5:16

72

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Show that the ideal $(2,f(x)) \subset \mathbb Z[x]$ is maximal for a given condition.

Published on 28 Mar 2026 - 10:16

144

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Sum of Algebraic number over $\mathbb{Q}$

Published on 01 Sep 2017 - 9:35

89

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What is the most right way to define irreducible polynomial over arbitrary ring?

Published on 03 Apr 2026 - 10:48

242

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Calculating Galois Group of $x^5+2x^2+2x+5$ over $\mathbb{Q}$

Published on 01 Sep 2017 - 21:22

205

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Showing a polynomial is irreducible in $\mathbb{Q}[x]$

Published on 02 Sep 2017 - 18:07

9.1k

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Show that $x^4-x^2+1$ is irreducible over $\mathbb{Q}$

Published on 02 Sep 2017 - 18:41

List Question

Primitive polynomial vs irreducible polynomial for construction field $GF(2)[x]/\langle p(x)\rangle$

Proof check: Irreducibility of $xy-1$

The splitting extention above Z_ (p)

Polynomial $x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1$ is reducible over $\mathbb{Q}$?

How to prove this polynomial is irreducible over $\mathbb{Q}$

Irreducible polynomial of degree $2$ over a finite field of characteristic $2$

A root of irreducible polynomial in field extension (proof)

Sufficient Conditions for (Ir)reducibility

Factorization and GCD for Rijndael's finite field

Show that the ideal $(2,f(x)) \subset \mathbb Z[x]$ is maximal for a given condition.

Sum of Algebraic number over $\mathbb{Q}$

What is the most right way to define irreducible polynomial over arbitrary ring?

Calculating Galois Group of $x^5+2x^2+2x+5$ over $\mathbb{Q}$

Showing a polynomial is irreducible in $\mathbb{Q}[x]$

Show that $x^4-x^2+1$ is irreducible over $\mathbb{Q}$

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