List questions from irreducible-polynomials

Published on 03 Sep 2017 - 13:34

145

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Show tht $f(x)$ is either irreducible or it splits in $F$.

Published on 03 Sep 2017 - 14:09

62

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Determining which finite fields a multi-variant polynomial has roots

Published on 04 Sep 2017 - 23:07

72

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Probably Primitive Polynomials Redux

Published on 06 Sep 2017 - 15:25

173

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$X^n-a$ is irreducible in $\mathbb{F}$ implies no zeros of $X^p-a$ in $\mathbb{F}$, $p|n, p<n$ a prime factor.

Published on 07 Sep 2017 - 12:51

126

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Does the sequence $f_1=x^2+1$ , $f_{n+1}=(f_n)^2+1$ contain only irreducible polynomials?

Published on 08 Sep 2017 - 10:59

206

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Why should I care about proving a polynomial to be irreducible?

Published on 26 Mar 2026 - 9:32

321

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Is $x^j+x^k+2$ irreducible whenever $j+k$ is odd?

Published on 09 Sep 2017 - 12:39

574

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Irreducible polynomial of degree 5 over the field of 2 elements has distinct roots in any algebraic closure of the field.

Published on 10 Sep 2017 - 14:46

125

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Solving for the value of $t$ in $4t^3-t-1=0$

Published on 13 Sep 2017 - 18:19

909

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Show that Q[x] /(x^2-2) is not isomorphic to Q[x] /(x^2-3)

Published on 06 Apr 2026 - 14:40

119

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$x^p - t$ has no roots in $\mathbb{F}_p(t)[x]$

Published on 16 Sep 2017 - 1:52

81

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Irreducibility of a polynomial with rational (polynomic) coefficients

Published on 16 Sep 2017 - 15:26

102

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Does this answer prove Cohn's sufficient irreducibility criterion?

Published on 16 Sep 2017 - 16:32

59

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Conjecture similar to Bunyakovsky-conjecture

Published on 19 Sep 2017 - 16:10

List Question

If one root is in then all roots are in

Show tht $f(x)$ is either irreducible or it splits in $F$.

Determining which finite fields a multi-variant polynomial has roots

Probably Primitive Polynomials Redux

$X^n-a$ is irreducible in $\mathbb{F}$ implies no zeros of $X^p-a$ in $\mathbb{F}$, $p|n, p<n$ a prime factor.

Does the sequence $f_1=x^2+1$ , $f_{n+1}=(f_n)^2+1$ contain only irreducible polynomials?

Why should I care about proving a polynomial to be irreducible?

Is $x^j+x^k+2$ irreducible whenever $j+k$ is odd?

Irreducible polynomial of degree 5 over the field of 2 elements has distinct roots in any algebraic closure of the field.

Solving for the value of $t$ in $4t^3-t-1=0$

Show that Q[x] /(x^2-2) is not isomorphic to Q[x] /(x^2-3)

$x^p - t$ has no roots in $\mathbb{F}_p(t)[x]$

Irreducibility of a polynomial with rational (polynomic) coefficients

Does this answer prove Cohn's sufficient irreducibility criterion?

Conjecture similar to Bunyakovsky-conjecture

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