Question

How to solve the equation $ x^{13} = 1$ by radicals? (And $x^{19}=1$)

score 735 · Answer 1 · 2016-05-20 23:24:23

735

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How to solve the equation $ x^{13} = 1$ by radicals? (And $x^{19}=1$)

Published on 20 May 2016 - 23:24

score 150 · Answer 2 · 2016-05-23 16:45:47

150

Views

How to solve the following solvable equation?

Published on 23 May 2016 - 16:45

score 681 · Answer 3 · 2016-05-27 08:29:43

681

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Determining the degree of a root of unity over a cyclotomic expansion

Published on 27 May 2016 - 8:29

score 218 · Answer 4 · 2016-05-31 11:43:02

218

Views

$\mathbb{Q}(\zeta_p)$ contains only one subfield $L$ such that $[L : \mathbb{Q}]=3$

Published on 31 May 2016 - 11:43

score 671 · Answer 5 · 2016-06-01 22:48:45

671

Views

Prove that $\phi_{2n}(X)=\phi_n(-X)$

Published on 01 Jun 2016 - 22:48

score 305 · Answer 6 · 2016-06-02 14:12:12

305

Views

Irreducibility of $X^5-7$ over $\mathbb{Q}(\sqrt[7]{2})[X]$ and degree of spitting field

Published on 02 Jun 2016 - 14:12

score 158 · Answer 7 · 2016-06-04 18:18:11

158

Views

Proof that $a^{n}+b^{n}$ is irreducible over $\mathbb Q$

Published on 04 Jun 2016 - 18:18

score 8k · Answer 8 · 2016-06-06 10:18:08

8k

Views

Prove that $X^4+X^3+X^2+X+1$ is irreducible in $\mathbb{Q}[X]$, but that it has two different irreducible factors in $\mathbb{R}[X]$

Published on 06 Jun 2016 - 10:18

score 1.1k · Answer 9 · 2016-06-07 12:10:39

1.1k

Views

How can I show that the Galois group of $x^p -1$ is abelian?

Published on 07 Jun 2016 - 12:10

score 271 · Answer 10 · 2016-06-19 14:57:22

271

Views

Primes is in P, proof of hendrik Lenstra Jr. lemma

Published on 19 Jun 2016 - 14:57

score 1k · Answer 11 · 2016-06-30 16:42:18

1k

Views

Are cyclotomic polynomials irreducible modulo a prime?

Published on 30 Jun 2016 - 16:42

score 537 · Answer 12 · 2013-04-04 14:57:23

537

Views

Show that for $n \geq 2$, the $n^{th}$ cyclotomic polynomial is a reciprocal polynomial, i.e. $\Phi_{n}(x) = x^{\phi(n)}\Phi(n)(x^{-1})$.

Published on 04 Apr 2013 - 14:57

score 296 · Answer 13 · 2013-04-05 15:21:21

296

Views

Why is the intersection of Q($\sqrt[n]{a}$) and Q(nth root of unity) Galois? (a>0, n an integer)

Published on 05 Apr 2013 - 15:21

score 1.2k · Answer 14 · 2013-04-06 21:49:18

1.2k

Views

Trace and cyclotomic field

Published on 06 Apr 2013 - 21:49

score 520 · Answer 15 · 2013-04-13 21:16:10

520

Views

$X^5 - 2$ is irreducible over $\mathbb{Q}[\zeta_5]$

Published on 13 Apr 2013 - 21:16

List Question

How to solve the equation $ x^{13} = 1$ by radicals? (And $x^{19}=1$)

How to solve the following solvable equation?

Determining the degree of a root of unity over a cyclotomic expansion

$\mathbb{Q}(\zeta_p)$ contains only one subfield $L$ such that $[L : \mathbb{Q}]=3$

Prove that $\phi_{2n}(X)=\phi_n(-X)$

Irreducibility of $X^5-7$ over $\mathbb{Q}(\sqrt[7]{2})[X]$ and degree of spitting field

Proof that $a^{n}+b^{n}$ is irreducible over $\mathbb Q$

Prove that $X^4+X^3+X^2+X+1$ is irreducible in $\mathbb{Q}[X]$, but that it has two different irreducible factors in $\mathbb{R}[X]$

How can I show that the Galois group of $x^p -1$ is abelian?

Primes is in P, proof of hendrik Lenstra Jr. lemma

Are cyclotomic polynomials irreducible modulo a prime?

Show that for $n \geq 2$, the $n^{th}$ cyclotomic polynomial is a reciprocal polynomial, i.e. $\Phi_{n}(x) = x^{\phi(n)}\Phi(n)(x^{-1})$.

Why is the intersection of Q($\sqrt[n]{a}$) and Q(nth root of unity) Galois? (a>0, n an integer)

Trace and cyclotomic field

$X^5 - 2$ is irreducible over $\mathbb{Q}[\zeta_5]$

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