List questions from irreducible-polynomials

Published on 13 Dec 2014 - 14:26

1.3k

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Irreducible in $F[x]$ implies irreducible in $R[x]$?

Published on 13 Dec 2014 - 22:53

329

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Is $\mathbb{Q}(\pi)$ a simple extension of $\mathbb{Q}\left(\frac{\pi^3}{1+\pi}\right)$?

Published on 14 Dec 2014 - 11:19

184

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Why is $T^4+6T^2-8T-3\in\mathbb Q[T]$ is irreducible?

Published on 14 Dec 2014 - 12:24

112

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Show that this polynomial is irreducible over Q

Published on 14 Dec 2014 - 14:30

588

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Prove particular quintic is irreducible

Published on 15 Dec 2014 - 4:52

138

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NTRU cryptosystem

Published on 27 Mar 2026 - 13:37

686

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Irreducibility of $~\frac{x^{6k+2}-x+1}{x^2-x+1}~$ over $\mathbb Q[x]$

Published on 26 Mar 2026 - 4:38

2.3k

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Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$

Published on 15 Dec 2014 - 17:11

28

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Sufficient condition for a polynomial to split

Published on 26 Mar 2026 - 8:14

3.6k

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A real number $x$ such that $x^n$ and $(x+1)^n$ are rational is itself rational

Published on 25 Mar 2026 - 17:40

115

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Irreducible in $\Bbb Q[x]$

Published on 16 Dec 2014 - 2:56

1.8k

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Getting the multiplicative inverse of a polynomial

Published on 16 Dec 2014 - 5:35

200

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Show that polynomial is reducible

Published on 18 Dec 2014 - 0:31

540

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How to factor polynomials in $\mathbb{Z}_n$?

Published on 18 Dec 2014 - 11:31

List Question

$p(x)$ divides the minimal polynomial iff $\exists v\ne 0: p(T)(v)=0$

Irreducible in $F[x]$ implies irreducible in $R[x]$?

Is $\mathbb{Q}(\pi)$ a simple extension of $\mathbb{Q}\left(\frac{\pi^3}{1+\pi}\right)$?

Why is $T^4+6T^2-8T-3\in\mathbb Q[T]$ is irreducible?

Show that this polynomial is irreducible over Q

Prove particular quintic is irreducible

NTRU cryptosystem

Irreducibility of $~\frac{x^{6k+2}-x+1}{x^2-x+1}~$ over $\mathbb Q[x]$

Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$

Sufficient condition for a polynomial to split

A real number $x$ such that $x^n$ and $(x+1)^n$ are rational is itself rational

Irreducible in $\Bbb Q[x]$

Getting the multiplicative inverse of a polynomial

Show that polynomial is reducible

How to factor polynomials in $\mathbb{Z}_n$?

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