List questions from irreducible-polynomials

Published on 15 Mar 2022 - 17:03

122

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Show that $x^2 + x + 2\in \mathbb{F}_5[x]$ is irreducible

Published on 17 Mar 2022 - 6:30

42

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A polynomial decomposition into a product of at least $n$ irreducible polynomials.

Published on 17 Mar 2022 - 11:03

63

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mod $p$ irreducibility test over $\mathbb{Z}$

Published on 11 Apr 2026 - 22:02

119

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Irreducibility of a quartic polynomial.

Published on 11 Apr 2026 - 4:00

55

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Equation with polynomial with integer coeficients.

Published on 09 Apr 2026 - 12:20

48

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Showing polynomial $p(x) = x^2 −3 \in\mathbb{F}_7[x]$ is prime in $E[x]$ and $x^3 - 2\in\mathbb{F}_7[x]$ factors into linear terms in $E$

Published on 30 Mar 2026 - 11:59

286

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Maximal degree of irreducible polynomials

Published on 11 Apr 2026 - 10:07

332

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How to prove that $p(x)$ is irreducible in $\mathbb{Q}(b)[x]$ if and only if $q(x)$ is irreducible in $\mathbb{Q}(a)[x]$

Published on 26 Mar 2022 - 19:11

351

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Decide if the polynomial $x^2-7$ is irreducible over $\mathbb Q, \mathbb R, \mathbb C$.

Published on 26 Mar 2022 - 23:25

126

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Showing that $x^2+y^2$ is irreducible in $k[x,y]$ provided that $\sqrt{-1}\notin k$

Published on 28 Mar 2022 - 18:16

73

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Proving irreducibility in $\Bbb Q[x]$

Published on 28 Mar 2022 - 20:55

107

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Binary Galois field, test for irreducible polynomial in NASA paper

Published on 14 Apr 2026 - 3:53

120

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Minimal polynomial of polynomial quotient field linear transfomation over finite field

Published on 13 Apr 2026 - 18:44

384

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Irreducible polynomial in field of positive characteristic

Published on 28 Mar 2026 - 8:35

List Question

Irreducible Polynomial in $\mathbb{F}_p (T) [x]$

Show that $x^2 + x + 2\in \mathbb{F}_5[x]$ is irreducible

A polynomial decomposition into a product of at least $n$ irreducible polynomials.

mod $p$ irreducibility test over $\mathbb{Z}$

Irreducibility of a quartic polynomial.

Equation with polynomial with integer coeficients.

Showing polynomial $p(x) = x^2 −3 \in\mathbb{F}_7[x]$ is prime in $E[x]$ and $x^3 - 2\in\mathbb{F}_7[x]$ factors into linear terms in $E$

Maximal degree of irreducible polynomials

How to prove that $p(x)$ is irreducible in $\mathbb{Q}(b)[x]$ if and only if $q(x)$ is irreducible in $\mathbb{Q}(a)[x]$

Decide if the polynomial $x^2-7$ is irreducible over $\mathbb Q, \mathbb R, \mathbb C$.

Showing that $x^2+y^2$ is irreducible in $k[x,y]$ provided that $\sqrt{-1}\notin k$

Proving irreducibility in $\Bbb Q[x]$

Binary Galois field, test for irreducible polynomial in NASA paper

Minimal polynomial of polynomial quotient field linear transfomation over finite field

Irreducible polynomial in field of positive characteristic

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