Question

Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$

score 1.1k · Answer 1 · 2015-05-29 22:46:01

1.1k

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Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$

Published on 29 May 2015 - 22:46

score 961 · Answer 2 · 2015-05-30 07:26:45

961

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Irreducibility of a cubic polynomial

Published on 30 May 2015 - 7:26

score 3k · Answer 3 · 2015-05-31 12:55:09

3k

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Showing that $x^4 -2x^2 +8 x+1$ is irreducible over $\Bbb Q$

Published on 31 May 2015 - 12:55

score 37 · Answer 4 · 2015-06-01 11:27:03

37

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Solve $\int (y^4+by^2+c)^{-1/2}dy=x$ as $y$ is a real valued function of $x$.

Published on 01 Jun 2015 - 11:27

score 230 · Answer 5 · 2015-06-02 09:18:16

230

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multiple roots of irreducible polynomial 2

Published on 02 Jun 2015 - 9:18

score 326 · Answer 6 · 2015-06-03 11:09:38

326

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Irreducibility of polynomials $x^{2^{n}}+1$

Published on 03 Jun 2015 - 11:09

score 2k · Answer 7 · 2015-06-03 12:20:24

2k

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Cases where irreducibility of polynomials over $\mathbb F \iff$ it has no roots in $\mathbb F $

Published on 03 Jun 2015 - 12:20

score 945 · Answer 8 · 2015-06-04 08:41:46

945

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Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$

Published on 04 Jun 2015 - 8:41

score 959 · Answer 9 · 2015-06-05 21:56:01

959

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Constructibility of roots of a polynomial

Published on 05 Jun 2015 - 21:56

score 49 · Answer 10 · 2015-06-10 02:03:24

49

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Let $K$ be a field and let $p(x)\in K[x]$ be an irreducible polynomial of degree $d$. Let $L = K[x]/p(x)$. Prove that $[L:K] = d$.

Published on 10 Jun 2015 - 2:03

score 187 · Answer 11 · 2015-06-10 09:41:37

187

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finding all irreducible polynomials over $\mathbb{F}_3$ up to degree $2$, faster method?

Published on 10 Jun 2015 - 9:41

score 441 · Answer 12 · 2026-03-26 22:54:12

441

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Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

Published on 26 Mar 2026 - 22:54

score 218 · Answer 13 · 2026-03-26 06:27:33

218

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Is this polynomial irreducible over the rationals?

Published on 26 Mar 2026 - 6:27

score 1.4k · Answer 14 · 2015-06-17 06:22:13

1.4k

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Prove the polynomial is irreducible

Published on 17 Jun 2015 - 6:22

score 4.2k · Answer 15 · 2026-04-01 16:56:40

4.2k

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Expansion of $x^n-y^n$

Published on 01 Apr 2026 - 16:56

List Question

Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$

Irreducibility of a cubic polynomial

Showing that $x^4 -2x^2 +8 x+1$ is irreducible over $\Bbb Q$

Solve $\int (y^4+by^2+c)^{-1/2}dy=x$ as $y$ is a real valued function of $x$.

multiple roots of irreducible polynomial 2

Irreducibility of polynomials $x^{2^{n}}+1$

Cases where irreducibility of polynomials over $\mathbb F \iff$ it has no roots in $\mathbb F $

Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$

Constructibility of roots of a polynomial

Let $K$ be a field and let $p(x)\in K[x]$ be an irreducible polynomial of degree $d$. Let $L = K[x]/p(x)$. Prove that $[L:K] = d$.

finding all irreducible polynomials over $\mathbb{F}_3$ up to degree $2$, faster method?

Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

Is this polynomial irreducible over the rationals?

Prove the polynomial is irreducible

Expansion of $x^n-y^n$

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