List questions from irreducible-polynomials

Published on 28 Mar 2024 - 15:28

48

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Polynomial for each extension degree

Published on 27 Mar 2026 - 17:04

102

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Why can't this happen in fields $K$ with $\operatorname{char}(K)=0$?

Published on 03 Jan 2015 - 18:22

176

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Degree of field extension $F_{p}(X^p,Y^p) \subset F_{p}(X,Y) $

Published on 04 Jan 2015 - 11:51

41

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Show T being prime element in $ F_{2}(T) $

Published on 04 Jan 2015 - 15:16

63

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possibility of trisection of angles

Published on 06 Jan 2015 - 13:27

127

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Root finding using Galois theory

Published on 07 Jan 2015 - 15:32

85

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If an irreducible $f(x)$ divides $f(x^2)$, then its splitting field is $F(\alpha)$ for any root $\alpha$ of $f(x)$?

Published on 27 Mar 2026 - 17:06

150

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An integer square matrix of prime order has size at least $(p-1)\times (p-1)$

Published on 08 Jan 2015 - 17:17

101

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Show that $x^4+n(2-n)x^2+n^2$ reducible over Q for any natural number n.

Published on 08 Jan 2015 - 19:33

381

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Back to Front Eisenstein - number theory

Published on 09 Jan 2015 - 0:25

91

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Factorize $x^4+n(2-n)x^2+n^2$ into irreducible polynomials over Q for any natural number n.

Published on 10 Jan 2015 - 9:59

57

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How do I prove the following theorem?

Published on 13 Jan 2015 - 17:29

2.7k

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How to factorize polynomial in GF(2)?

Published on 15 Jan 2015 - 7:38

151

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Irreducible polynomial with three real zeros

Published on 17 Jan 2015 - 1:11

List Question

Irreducible polynomial in $\Bbb{Z}_2[x]$

Polynomial for each extension degree

Why can't this happen in fields $K$ with $\operatorname{char}(K)=0$?

Degree of field extension $F_{p}(X^p,Y^p) \subset F_{p}(X,Y) $

Show T being prime element in $ F_{2}(T) $

possibility of trisection of angles

Root finding using Galois theory

If an irreducible $f(x)$ divides $f(x^2)$, then its splitting field is $F(\alpha)$ for any root $\alpha$ of $f(x)$?

An integer square matrix of prime order has size at least $(p-1)\times (p-1)$

Show that $x^4+n(2-n)x^2+n^2$ reducible over Q for any natural number n.

Back to Front Eisenstein - number theory

Factorize $x^4+n(2-n)x^2+n^2$ into irreducible polynomials over Q for any natural number n.

How do I prove the following theorem?

How to factorize polynomial in GF(2)?

Irreducible polynomial with three real zeros

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