Question

A question about quadratic non-residues in finite fields.

score 58 · Answer 1 · 2026-03-27 23:20:11

58

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A question about quadratic non-residues in finite fields.

Published on 27 Mar 2026 - 23:20

score 69 · Answer 2 · 2026-03-27 18:09:29

69

Views

Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

Published on 27 Mar 2026 - 18:09

score 42 · Answer 3 · 2019-01-18 11:12:09

42

Views

Simple field extension where primitive element is algebraic

Published on 18 Jan 2019 - 11:12

score 305 · Answer 4 · 2019-01-19 03:06:01

305

Views

What is the probability that a rational prime remains prime in $\mathbb Z[i,\sqrt{-3}]$?

Published on 19 Jan 2019 - 3:06

score 1.3k · Answer 5 · 2019-01-21 00:47:20

1.3k

Views

Let $E$ be an algebraically closed extension field of a field $F$. Show that the algebraic closure $\bar F_E$ of $F$ in $E$ is algebraically closed.

Published on 21 Jan 2019 - 0:47

score 101 · Answer 6 · 2019-01-22 05:58:36

101

Views

Is the field of complex numbers the field of rational functions over a subfield?

Published on 22 Jan 2019 - 5:58

score 2.2k · Answer 7 · 2019-01-23 13:17:24

2.2k

Views

Degree of the extension $\mathbb{Q}(\sqrt{3 + 2\sqrt{2}})$.

Published on 23 Jan 2019 - 13:17

score 116 · Answer 8 · 2019-01-23 21:22:13

116

Views

$K \subset L$ a field extension and $L$ algebraically closed implies that $A$ is the algebraic closure of $K$

Published on 23 Jan 2019 - 21:22

score 123 · Answer 9 · 2019-01-24 06:16:32

123

Views

Use linear algebra to find an $n$th-degree polynomial with a zero at $x = \sqrt{3} + \sqrt{5} + \sqrt{3 + 4\sqrt{5}}$.

Published on 24 Jan 2019 - 6:16

score 123 · Answer 10 · 2026-03-25 07:56:47

123

Views

Binary matrix with fixed inner product.

Published on 25 Mar 2026 - 7:56

score 159 · Answer 11 · 2026-03-27 18:14:54

159

Views

Degree of extension - Is this $\phi(n)$ or $\phi(n)/2$?

Published on 27 Mar 2026 - 18:14

score 48 · Answer 12 · 2019-01-25 23:44:20

48

Views

How to find the dimension of this field extension?

Published on 25 Jan 2019 - 23:44

score 58 · Answer 13 · 2019-01-28 04:00:24

58

Views

Extended field for $u^2+1$

Published on 28 Jan 2019 - 4:00

score 169 · Answer 14 · 2026-03-26 13:51:38

169

Views

irreducibility of polynomial over field of rational functions

Published on 26 Mar 2026 - 13:51

score 2.8k · Answer 15 · 2026-03-28 05:00:40

2.8k

Views

"Numbers" bigger than every natural number

Published on 28 Mar 2026 - 5:00

List Question

A question about quadratic non-residues in finite fields.

Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

Simple field extension where primitive element is algebraic

What is the probability that a rational prime remains prime in $\mathbb Z[i,\sqrt{-3}]$?

Let $E$ be an algebraically closed extension field of a field $F$. Show that the algebraic closure $\bar F_E$ of $F$ in $E$ is algebraically closed.

Is the field of complex numbers the field of rational functions over a subfield?

Degree of the extension $\mathbb{Q}(\sqrt{3 + 2\sqrt{2}})$.

$K \subset L$ a field extension and $L$ algebraically closed implies that $A$ is the algebraic closure of $K$

Use linear algebra to find an $n$th-degree polynomial with a zero at $x = \sqrt{3} + \sqrt{5} + \sqrt{3 + 4\sqrt{5}}$.

Binary matrix with fixed inner product.

Degree of extension - Is this $\phi(n)$ or $\phi(n)/2$?

How to find the dimension of this field extension?

Extended field for $u^2+1$

irreducibility of polynomial over field of rational functions

"Numbers" bigger than every natural number

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