Question

Let $\alpha = 2\cos(\frac{2\pi}{7})$. What is the minimal polynomial of $\alpha$ over $\mathbb{Q}$?

score 146 · Answer 1 · 2026-04-15 02:51:12

146

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Let $\alpha = 2\cos(\frac{2\pi}{7})$. What is the minimal polynomial of $\alpha$ over $\mathbb{Q}$?

Published on 15 Apr 2026 - 2:51

score 69 · Answer 2 · 2026-04-11 16:01:42

69

Views

How do you solve irreducible, solvable degree 11 polynomials using langrange resolvents?

Published on 11 Apr 2026 - 16:01

score 35 · Answer 3 · 2026-04-11 09:52:49

35

Views

Transforming an irreducible polynomial $f(x)$ to $g(X)$ that is reducible (over $\mathbb{Z}$)

Published on 11 Apr 2026 - 9:52

score 52 · Answer 4 · 2026-04-14 23:59:53

52

Views

Examples of coprime polynomials $f(x)^3+g(x)^2=h(x)$ with $6\deg h<\deg g$

Published on 14 Apr 2026 - 23:59

score 182 · Answer 5 · 2026-04-14 02:46:23

182

Views

When are the roots of polynomials with rational coefficients rationally independent?

Published on 14 Apr 2026 - 2:46

score 222 · Answer 6 · 2026-04-14 03:37:09

222

Views

Ideal of functions vanishing on a plane algebraic curve

Published on 14 Apr 2026 - 3:37

score 268 · Answer 7 · 2022-10-13 08:49:37

268

Views

Why can't wolfram alpha solve this simple quintic?

Published on 13 Oct 2022 - 8:49

score 210 · Answer 8 · 2026-04-10 18:33:34

210

Views

$\sum{x^{(i,n)}}+1$ is irreducible?

Published on 10 Apr 2026 - 18:33

score 38 · Answer 9 · 2026-04-13 23:21:14

38

Views

uniqueness of irreducible polynomials in a Galois field

Published on 13 Apr 2026 - 23:21

score 36 · Answer 10 · 2022-10-15 13:31:19

36

Views

For what primes $p$ is the mod 2 polynomial $(x^p-1)/(x-1)$ irreducible? Are there simple criteria?

Published on 15 Oct 2022 - 13:31

score 107 · Answer 11 · 2022-10-17 07:05:24

107

Views

Study irreducibility of $f(x) = x^{20} + 5x^{15}+25x^{10}+125x^5+625$ in $\mathbb Q[x]$

Published on 17 Oct 2022 - 7:05

score 154 · Answer 12 · 2026-04-15 00:27:14

154

Views

$f$ is irreducible over $\mathbb Q_p$ if its Newton polygon consists of one segment

Published on 15 Apr 2026 - 0:27

score 395 · Answer 13 · 2022-10-22 22:20:36

395

Views

Find the real root of the almost symmetric polynomial $x^7+7x^5+14x^3+7x-1$

Published on 22 Oct 2022 - 22:20

score 631 · Answer 14 · 2026-04-14 04:42:29

631

Views

Under the which condition, factorisation of $a_1^n+a_2^n+\cdots+a_n^n-na_1a_2a_3...a_n ?$ is possible?

Published on 14 Apr 2026 - 4:42

score 83 · Answer 15 · 2026-04-12 09:11:40

83

Views

Finding irreducible polynomial over the rationals

Published on 12 Apr 2026 - 9:11

List Question

Let $\alpha = 2\cos(\frac{2\pi}{7})$. What is the minimal polynomial of $\alpha$ over $\mathbb{Q}$?

How do you solve irreducible, solvable degree 11 polynomials using langrange resolvents?

Transforming an irreducible polynomial $f(x)$ to $g(X)$ that is reducible (over $\mathbb{Z}$)

Examples of coprime polynomials $f(x)^3+g(x)^2=h(x)$ with $6\deg h<\deg g$

When are the roots of polynomials with rational coefficients rationally independent?

Ideal of functions vanishing on a plane algebraic curve

Why can't wolfram alpha solve this simple quintic?

$\sum{x^{(i,n)}}+1$ is irreducible?

uniqueness of irreducible polynomials in a Galois field

For what primes $p$ is the mod 2 polynomial $(x^p-1)/(x-1)$ irreducible? Are there simple criteria?

Study irreducibility of $f(x) = x^{20} + 5x^{15}+25x^{10}+125x^5+625$ in $\mathbb Q[x]$

$f$ is irreducible over $\mathbb Q_p$ if its Newton polygon consists of one segment

Find the real root of the almost symmetric polynomial $x^7+7x^5+14x^3+7x-1$

Under the which condition, factorisation of $a_1^n+a_2^n+\cdots+a_n^n-na_1a_2a_3...a_n ?$ is possible?

Finding irreducible polynomial over the rationals

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