List questions from irreducible-polynomials

Published on 07 Oct 2013 - 11:04

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Questions about field extensions and irreducibility

Published on 09 Oct 2013 - 10:11

513

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Find the irreducible factors of $f(x)=x^4-5x^2+6$ over $\mathbb{Q}$ and over $\mathbb{R}$ individually.

Published on 11 Oct 2013 - 6:18

153

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Is it necessarily true that if a polynomial is irreducible in $\mathbb Z_n$ ($n$ is prime) then it is irreducible in $\mathbb{Q}$?

Published on 13 Oct 2013 - 5:57

2.7k

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Rabin's test for polynomial irreducibility over $\mathbb{F}_2$

Published on 16 Oct 2013 - 14:19

589

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Prove that a function is irreducible

Published on 18 Oct 2013 - 23:19

27.2k

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showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$

Published on 27 Mar 2026 - 7:49

1.6k

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convert from polynomial to normal base in GF(2^5)

Published on 20 Oct 2013 - 15:51

9.4k

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When is a cyclotomic polynomial over a finite field a minimal polynomial?

Published on 27 Mar 2026 - 7:49

1.3k

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Quotient $K[x,y]/(f)$, $f$ irreducible, which is not UFD

Published on 29 Mar 2026 - 19:17

3.8k

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How many irreducible factors does $x^n-1$ have over finite field?

Published on 22 Oct 2013 - 13:34

263

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Is the polynomial $x^{p^n} + 1$ irreducible in $\mathbb Q[x]$ when $ p$ is prime and odd?

Published on 22 Oct 2013 - 14:03

198

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Find an irreducible polynomial with zero $\cos(2\pi/7)$

Published on 23 Oct 2013 - 0:47

195

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A problem about irreducible polynomials in two indeterminates over a field

Published on 23 Oct 2013 - 2:02

303

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Another problem about irreducible polynomials over a (finite) field

Published on 23 Oct 2013 - 3:09

List Question

Is $x^8+1$ irreducible in $\mathbb{R}[x]$

Questions about field extensions and irreducibility

Find the irreducible factors of $f(x)=x^4-5x^2+6$ over $\mathbb{Q}$ and over $\mathbb{R}$ individually.

Is it necessarily true that if a polynomial is irreducible in $\mathbb Z_n$ ($n$ is prime) then it is irreducible in $\mathbb{Q}$?

Rabin's test for polynomial irreducibility over $\mathbb{F}_2$

Prove that a function is irreducible

showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$

convert from polynomial to normal base in GF(2^5)

When is a cyclotomic polynomial over a finite field a minimal polynomial?

Quotient $K[x,y]/(f)$, $f$ irreducible, which is not UFD

How many irreducible factors does $x^n-1$ have over finite field?

Is the polynomial $x^{p^n} + 1$ irreducible in $\mathbb Q[x]$ when $ p$ is prime and odd?

Find an irreducible polynomial with zero $\cos(2\pi/7)$

A problem about irreducible polynomials in two indeterminates over a field

Another problem about irreducible polynomials over a (finite) field

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