List questions from irreducible-polynomials

29

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$\underset{\bar{a},\bar{b}\in S^n}{Pr}[f(x,\bar{a}t+\bar{b})\text{ is reducible and }f(x,\bar{b})\text{ is square-free}]\leq\frac{7d^6}{|S|}$

Published on 25 Mar 2026 - 14:35

64

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Over prime fields, are all monic irreducible polynomials primitive?

Published on 15 Apr 2026 - 12:09

95

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Factorize $(X+1)^{101}+100$ in irreducibles in $\mathbb{Q}[X]$.

Published on 23 Dec 2022 - 15:57

152

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$x^2-y^2-1$ irreducible in $K[x,y]$

Published on 14 Apr 2026 - 21:03

179

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Galois group of $x^n+x+1$

Published on 15 Apr 2026 - 8:40

155

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Splitting field of a degree 3 polynomial is generated by a root and the square root of the discriminant

Published on 13 Apr 2026 - 0:09

125

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The subgroups in this Hasse diagram represent which field extension?

Published on 14 Apr 2026 - 18:15

540

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Showing $x^4 + 1$ is irreducible in $\mathbb{Q}[x]$.

Published on 02 Jan 2023 - 23:12

97

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Proof Check of Irreducibility of $x^2 +1$ in a field.

Published on 14 Apr 2026 - 20:09

113

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Prove that the determinant is irreducible

Published on 15 Apr 2026 - 11:43

99

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Circulant determinant factorization over Z

Published on 25 Mar 2026 - 17:26

46

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Show that $A=cI$ for c non-zero real number.

Published on 14 Apr 2026 - 17:59

70

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How to know if this polynomial is irreducible

Published on 11 Apr 2026 - 3:42

148

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Primitive Polynomials over $\mathbb{Z}_3$

Published on 13 Apr 2026 - 2:10

168

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Find all rational numbers $r\in\mathbb{Q}$ s.t. $\cos(r\cdot\pi)$ is rational

Published on 12 Apr 2026 - 8:57

List Question

$\underset{\bar{a},\bar{b}\in S^n}{Pr}[f(x,\bar{a}t+\bar{b})\text{ is reducible and }f(x,\bar{b})\text{ is square-free}]\leq\frac{7d^6}{|S|}$

Over prime fields, are all monic irreducible polynomials primitive?

Factorize $(X+1)^{101}+100$ in irreducibles in $\mathbb{Q}[X]$.

$x^2-y^2-1$ irreducible in $K[x,y]$

Galois group of $x^n+x+1$

Splitting field of a degree 3 polynomial is generated by a root and the square root of the discriminant

The subgroups in this Hasse diagram represent which field extension?

Showing $x^4 + 1$ is irreducible in $\mathbb{Q}[x]$.

Proof Check of Irreducibility of $x^2 +1$ in a field.

Prove that the determinant is irreducible

Circulant determinant factorization over Z

Show that $A=cI$ for c non-zero real number.

How to know if this polynomial is irreducible

Primitive Polynomials over $\mathbb{Z}_3$

Find all rational numbers $r\in\mathbb{Q}$ s.t. $\cos(r\cdot\pi)$ is rational

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