Question

How to prove $[\mathbb Q(\zeta_{p^k}): \mathbb Q] = (p-1)*p^{k-1}$?

score 26 · Answer 1 · 2013-06-19 09:03:26

26

Views

How to prove $[\mathbb Q(\zeta_{p^k}): \mathbb Q] = (p-1)*p^{k-1}$?

Published on 19 Jun 2013 - 9:03

score 19k · Answer 2 · 2013-06-23 10:35:04

19k

Views

Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime

Published on 23 Jun 2013 - 10:35

score 703 · Answer 3 · 2026-03-27 06:08:52

703

Views

Is $\bigl(X(X-a)(X-b)\bigr)^{2^n} +1$ an irreducible polynomial over $\mathbb{Q}[X]$?

Published on 27 Mar 2026 - 6:08

score 847 · Answer 4 · 2026-04-02 04:08:13

847

Views

Is $2+5x$ a primitive root in $\mathbb{F}_7[x]/(x^2+1)$?

Published on 02 Apr 2026 - 4:08

score 238 · Answer 5 · 2013-07-12 08:04:28

238

Views

Prove that every irreducible cubic monic polynomial over $\mathbb F_{5}$ has the form $P_{t}(x)=(x-t_{1})(x-t_{2})(x-t_{3})+t_{0}(x-t_{4})(x-t_{5})$?

Published on 12 Jul 2013 - 8:04

score 117 · Answer 6 · 2013-07-14 15:16:45

117

Views

About irreducibility of a particular class of bihomogeneous polynomials

Published on 14 Jul 2013 - 15:16

score 2.4k · Answer 7 · 2013-07-14 20:10:48

2.4k

Views

Proving irreducibility of $x^6-72$

Published on 14 Jul 2013 - 20:10

score 130 · Answer 8 · 2013-07-15 02:29:00

130

Views

Are these polynomials irreducible in $\mathbb{Q}[x]$?

Published on 15 Jul 2013 - 2:29

score 84 · Answer 9 · 2013-07-16 23:18:38

84

Views

Prove that if the coefficient of $ax^3+bx+c$ are odd then it is irreducible of $\mathbb{Q}$

Published on 16 Jul 2013 - 23:18

score 167 · Answer 10 · 2013-07-27 07:57:22

167

Views

How to show that $x^6-72$ is irreducible over the rationals?

Published on 27 Jul 2013 - 7:57

score 3.8k · Answer 11 · 2013-08-03 14:23:03

3.8k

Views

Irreducibility check for polynomials not satisfying Eisenstein Criterion.

Published on 03 Aug 2013 - 14:23

score 449 · Answer 12 · 2013-08-04 00:15:22

449

Views

If $F(a_1,\ldots,a_k)=0$ whenever $a_1,\ldots,a_k$ are integers such that $f(x)=x^k-a_1x^{k-1}-\cdots-a_k$ is irreducible, then $F\equiv0$

Published on 04 Aug 2013 - 0:15

score 651 · Answer 13 · 2013-08-04 05:05:28

651

Views

Irreducibility conditions mod $n$

Published on 04 Aug 2013 - 5:05

score 143 · Answer 14 · 2013-08-06 15:16:59

143

Views

Conjugates of $12^{1/5}+54^{1/5}-144^{1/5}+648^{1/5}$ over $\mathbb{Q}$

Published on 06 Aug 2013 - 15:16

score 601 · Answer 15 · 2013-08-07 09:04:54

601

Views

Prove that $f(x)$ is irreducible over $\mathbb{Q}$ (rational field).

Published on 07 Aug 2013 - 9:04

List Question

How to prove $[\mathbb Q(\zeta_{p^k}): \mathbb Q] = (p-1)*p^{k-1}$?

Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime

Is $\bigl(X(X-a)(X-b)\bigr)^{2^n} +1$ an irreducible polynomial over $\mathbb{Q}[X]$?

Is $2+5x$ a primitive root in $\mathbb{F}_7[x]/(x^2+1)$?

Prove that every irreducible cubic monic polynomial over $\mathbb F_{5}$ has the form $P_{t}(x)=(x-t_{1})(x-t_{2})(x-t_{3})+t_{0}(x-t_{4})(x-t_{5})$?

About irreducibility of a particular class of bihomogeneous polynomials

Proving irreducibility of $x^6-72$

Are these polynomials irreducible in $\mathbb{Q}[x]$?

Prove that if the coefficient of $ax^3+bx+c$ are odd then it is irreducible of $\mathbb{Q}$

How to show that $x^6-72$ is irreducible over the rationals?

Irreducibility check for polynomials not satisfying Eisenstein Criterion.

If $F(a_1,\ldots,a_k)=0$ whenever $a_1,\ldots,a_k$ are integers such that $f(x)=x^k-a_1x^{k-1}-\cdots-a_k$ is irreducible, then $F\equiv0$

Irreducibility conditions mod $n$

Conjugates of $12^{1/5}+54^{1/5}-144^{1/5}+648^{1/5}$ over $\mathbb{Q}$

Prove that $f(x)$ is irreducible over $\mathbb{Q}$ (rational field).

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