List questions from irreducible-polynomials

Published on 29 Jan 2019 - 15:34

161

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Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

Published on 25 Mar 2026 - 19:32

839

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Is the polynomial $x^4+10x^2+1$ reducible over $\mathbb{Z}[x]$?

Published on 31 Jan 2019 - 15:42

2.2k

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The polynomial $x^6+x^3+1$ is irreducible over $\mathbb{Q}[x]$

Published on 31 Jan 2019 - 16:21

1.7k

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$x^2+y^2-1$ is irreducible in $\mathbb{Q}[x,y]$.

Published on 31 Jan 2019 - 16:41

326

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Probability that an irreducible polynomial has a root modulo a prime $p$

Published on 03 Feb 2019 - 1:00

149

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A problem of factoring a polynomial with a hint

Published on 03 Feb 2019 - 3:53

231

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A consequence of Gauss' lemma

Published on 25 Mar 2026 - 7:41

425

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Prove that $x^{5}-x+a$ is an irreducible polynomial

Published on 05 Feb 2019 - 3:48

84

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If $\sigma^{*}\left(p\left(x\right)\right)$ is irreducible in $S\left[x\right]$, then $p\left(x\right)$ is irreducible in $R\left[x\right]$.

Published on 25 Mar 2026 - 6:06

114

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Primes $p=n^6+1$

Published on 26 Mar 2026 - 4:50

59

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Irreducible elements in a factor ring

Published on 05 Feb 2019 - 20:18

55

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Polynomials taking a prime or 1 value on infinitely many points are irreducible

Published on 26 Mar 2026 - 1:08

186

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Proof of "Lagrange Lemma"

Published on 07 Feb 2019 - 16:37

46

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How to show that a given polynomial is irreducible in a cyclotomic field

Published on 25 Mar 2026 - 1:28

List Question

irreducibility of polynomial over field of rational functions

Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

Is the polynomial $x^4+10x^2+1$ reducible over $\mathbb{Z}[x]$?

The polynomial $x^6+x^3+1$ is irreducible over $\mathbb{Q}[x]$

$x^2+y^2-1$ is irreducible in $\mathbb{Q}[x,y]$.

Probability that an irreducible polynomial has a root modulo a prime $p$

A problem of factoring a polynomial with a hint

A consequence of Gauss' lemma

Prove that $x^{5}-x+a$ is an irreducible polynomial

If $\sigma^{*}\left(p\left(x\right)\right)$ is irreducible in $S\left[x\right]$, then $p\left(x\right)$ is irreducible in $R\left[x\right]$.

Primes $p=n^6+1$

Irreducible elements in a factor ring

Polynomials taking a prime or 1 value on infinitely many points are irreducible

Proof of "Lagrange Lemma"

How to show that a given polynomial is irreducible in a cyclotomic field

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