List questions from irreducible-polynomials

73

Views

Let $p(x) = x^3 + x + 1 \in \mathbb Z_2[x]$ and $E = \mathbb Z_2[x]/p(x)$. Factor $p(x)$ into linear factors in $E[x]$.

Published on 10 May 2026 - 12:54

355

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Basis over GF(2^5) with sum of its elements = 1

Published on 14 Apr 2026 - 21:30

295

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Irreducible polynomial over $GF(32)$

Published on 14 Apr 2026 - 18:06

306

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Is $f(y) = 5 - 4y^2 + y^4$ irreducible over $\mathbb{Q}(\sqrt{5})$?

Published on 16 Apr 2026 - 9:10

229

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There are infinitely prime numbers $p$, st $P(x)+p$ is irreducible over $\mathbb{Z}[x]$

Published on 14 Apr 2026 - 8:54

38

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$f(x)=x^{p^n}-b$ is irreducible

Published on 16 Apr 2026 - 0:22

50

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$x^2-2$ is irreducible in $\mathbb{Q}[x]$ implies that $\mathbb{Q}[\sqrt{2}]$ is a field

Published on 17 Apr 2026 - 3:15

1k

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Irreducibility using Fermat's Little Theorem

Published on 11 Apr 2026 - 13:21

441

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Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?

Published on 13 Apr 2026 - 23:40

108

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Doubly transitive Galois group

Published on 14 Apr 2026 - 1:08

92

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How to show that, the Galois Group is doubly transitive.

Published on 10 Apr 2026 - 17:35

133

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Proof, that factor of irreducible polynomial is irreducible over field defined by root of irreducible

Published on 12 Apr 2026 - 3:10

86

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What is $(x^7-x)mod(x^6-3)$ equal to?

Published on 15 Apr 2026 - 20:36

86

Views

A question on Finite fields and irreducible polynomials.

Published on 10 May 2026 - 19:35

63

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Polynomial divibility over finite field

Published on 11 Apr 2026 - 20:12

List Question

Let $p(x) = x^3 + x + 1 \in \mathbb Z_2[x]$ and $E = \mathbb Z_2[x]/p(x)$. Factor $p(x)$ into linear factors in $E[x]$.

Basis over GF(2^5) with sum of its elements = 1

Irreducible polynomial over $GF(32)$

Is $f(y) = 5 - 4y^2 + y^4$ irreducible over $\mathbb{Q}(\sqrt{5})$?

There are infinitely prime numbers $p$, st $P(x)+p$ is irreducible over $\mathbb{Z}[x]$

$f(x)=x^{p^n}-b$ is irreducible

$x^2-2$ is irreducible in $\mathbb{Q}[x]$ implies that $\mathbb{Q}[\sqrt{2}]$ is a field

Irreducibility using Fermat's Little Theorem

Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?

Doubly transitive Galois group

How to show that, the Galois Group is doubly transitive.

Proof, that factor of irreducible polynomial is irreducible over field defined by root of irreducible

What is $(x^7-x)mod(x^6-3)$ equal to?

A question on Finite fields and irreducible polynomials.

Polynomial divibility over finite field

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