Question

Smart way to solve octics like $x^8+5992704x-304129728=0$

score 336 · Answer 1 · 2026-03-25 11:16:17

336

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Smart way to solve octics like $x^8+5992704x-304129728=0$

Published on 25 Mar 2026 - 11:16

score 31 · Answer 2 · 2018-12-23 16:16:44

31

Views

Criterion for a splitting field of a quadratic polynomial to be a Galois Extension

Published on 23 Dec 2018 - 16:16

score 35 · Answer 3 · 2026-03-27 19:44:33

35

Views

There is an integer $l$ such that $f_l = x^{2^l}+1$ is reducible in $\mathbb{F}_p[x]$ for any prime $p$

Published on 27 Mar 2026 - 19:44

score 79 · Answer 4 · 2018-12-23 16:48:04

79

Views

Proving a theorem in Galois Theory in a strange manner. Is the following proof valid?

Published on 23 Dec 2018 - 16:48

score 920 · Answer 5 · 2026-03-25 19:03:39

920

Views

Computing primitive roots of unity in a Finite Field extension

Published on 25 Mar 2026 - 19:03

score 809 · Answer 6 · 2018-12-23 21:51:06

809

Views

How Did Galois Understand the Galois Group?

Published on 23 Dec 2018 - 21:51

score 814 · Answer 7 · 2026-03-25 17:52:07

814

Views

Compute the degree of the splitting field of $x^{12} - 2$ over $\mathbb{Q}$ and describe its Galois Group as a semidirect product

Published on 25 Mar 2026 - 17:52

score 404 · Answer 8 · 2018-12-24 22:12:07

404

Views

Galois group of a certain splitting field

Published on 24 Dec 2018 - 22:12

score 305 · Answer 9 · 2026-03-25 06:19:12

305

Views

Galois Groups in Ramification Theory

Published on 25 Mar 2026 - 6:19

score 296 · Answer 10 · 2018-12-25 19:43:54

296

Views

Degree of $a+b$ over a field $k$, where $a$ and $b$ are distinct roots of the same polynomial

Published on 25 Dec 2018 - 19:43

score 3.6k · Answer 11 · 2026-03-26 11:08:11

3.6k

Views

Showing $S_{n}$ is not solvable for $n\geq 5$

Published on 26 Mar 2026 - 11:08

score 303 · Answer 12 · 2018-12-26 02:59:16

303

Views

Existence of $n$ distinct roots of a set of polynomials

Published on 26 Dec 2018 - 2:59

score 189 · Answer 13 · 2018-12-26 17:14:24

189

Views

Missing step in proving that $[L:K] = n \Rightarrow$ there are precisely $n$ distinct $K$-monomorphisms $L \rightarrow N$.

Published on 26 Dec 2018 - 17:14

score 243 · Answer 14 · 2026-03-27 13:01:58

243

Views

Show that if $K \subseteq M \subseteq L$, then the normal closure $N'$ of $L:M$ is contained in the normal closure $N$ of $L:K$.

Published on 27 Mar 2026 - 13:01

score 122 · Answer 15 · 2026-03-27 18:14:52

122

Views

Primes lying above a prime in a Galois extension

Published on 27 Mar 2026 - 18:14

List Question

Smart way to solve octics like $x^8+5992704x-304129728=0$

Criterion for a splitting field of a quadratic polynomial to be a Galois Extension

There is an integer $l$ such that $f_l = x^{2^l}+1$ is reducible in $\mathbb{F}_p[x]$ for any prime $p$

Proving a theorem in Galois Theory in a strange manner. Is the following proof valid?

Computing primitive roots of unity in a Finite Field extension

How Did Galois Understand the Galois Group?

Compute the degree of the splitting field of $x^{12} - 2$ over $\mathbb{Q}$ and describe its Galois Group as a semidirect product

Galois group of a certain splitting field

Galois Groups in Ramification Theory

Degree of $a+b$ over a field $k$, where $a$ and $b$ are distinct roots of the same polynomial

Showing $S_{n}$ is not solvable for $n\geq 5$

Existence of $n$ distinct roots of a set of polynomials

Missing step in proving that $[L:K] = n \Rightarrow$ there are precisely $n$ distinct $K$-monomorphisms $L \rightarrow N$.

Show that if $K \subseteq M \subseteq L$, then the normal closure $N'$ of $L:M$ is contained in the normal closure $N$ of $L:K$.

Primes lying above a prime in a Galois extension

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