List questions from irreducible-polynomials

Published on 05 Feb 2024 - 19:51

60

Views

A polynomial in $\mathbb Z[x]$ not generated by $5$ and $x^2+2$.

Published on 07 Feb 2024 - 20:25

52

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Is $X^3+2Y^2+3\in \mathbb{Q}[X,Y]$ prime?

Published on 01 Apr 2026 - 18:14

105

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Degree-$p$ étale covers of affine line

Published on 25 Mar 2026 - 15:28

24

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Probability that an integer polynomial factors in a particular family

Published on 23 Feb 2026 - 1:39

58

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How to check whether $f(X)=X^4-6X^2+1$ is irreducible or not in $\mathbb{Q}[X]$?

Published on 11 Feb 2024 - 21:59

49

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A polynomial in two variables is irreducible

Published on 13 Feb 2024 - 16:46

67

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Number of real roots of $f(x) = (x^6) + 2(x^4) + (x^2) - 2(x) + 1$

Published on 16 Feb 2024 - 2:55

71

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Rational polynomial $f$ of minimal degree such that $f(x^{d-1},y^{d-1},z^{d-1})$ is divisible by $x^d+y^d+z^d$

Published on 28 Mar 2026 - 15:21

17

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Irreducibility of random polynomials with coefficients distributed according to some probability measure

Published on 13 Mar 2026 - 10:40

128

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Show that $x^5+x^3+x+1$ is irreducible over $\mathbb Q$.

Published on 29 Feb 2024 - 14:58

62

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Every subring of a field is an integral domain

Published on 01 Apr 2026 - 18:09

37

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divisibility in polynomial ring: if $(X - a)^t | f(X)$ and $(X - b)^t | f(X)$, then does $(X - a)^t \cdot (X - b)^t \mid f(X)$?

Published on 25 Mar 2026 - 23:42

100

Views

Irreducible $p(x) \in \mathbb{Q}[X]$ with roots $r, s$ such that $rs = 1$.

Published on 07 Mar 2024 - 5:19

46

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Reducing an inseparable polynomial over the same field to a separable polynomial over a field

Published on 23 Feb 2026 - 12:02

List Question

Show degree of minimal polynomial has to be even

A polynomial in $\mathbb Z[x]$ not generated by $5$ and $x^2+2$.

Is $X^3+2Y^2+3\in \mathbb{Q}[X,Y]$ prime?

Degree-$p$ étale covers of affine line

Probability that an integer polynomial factors in a particular family

How to check whether $f(X)=X^4-6X^2+1$ is irreducible or not in $\mathbb{Q}[X]$?

A polynomial in two variables is irreducible

Number of real roots of $f(x) = (x^6) + 2(x^4) + (x^2) - 2(x) + 1$

Rational polynomial $f$ of minimal degree such that $f(x^{d-1},y^{d-1},z^{d-1})$ is divisible by $x^d+y^d+z^d$

Irreducibility of random polynomials with coefficients distributed according to some probability measure

Show that $x^5+x^3+x+1$ is irreducible over $\mathbb Q$.

Every subring of a field is an integral domain

divisibility in polynomial ring: if $(X - a)^t | f(X)$ and $(X - b)^t | f(X)$, then does $(X - a)^t \cdot (X - b)^t \mid f(X)$?

Irreducible $p(x) \in \mathbb{Q}[X]$ with roots $r, s$ such that $rs = 1$.

Reducing an inseparable polynomial over the same field to a separable polynomial over a field

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