Question

How to prove that one of $2,3,6$ is a square modulo every prime $p$?

score 638 · Answer 1 · 2026-04-13 10:14:28

638

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How to prove that one of $2,3,6$ is a square modulo every prime $p$?

Published on 13 Apr 2026 - 10:14

score 128 · Answer 2 · 2026-04-14 06:58:08

128

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Hasse's classification of Quaternion algebras (over number fields)

Published on 14 Apr 2026 - 6:58

score 317 · Answer 3 · 2026-04-11 18:20:55

317

Views

Commutativity of $End(E)$ for $E$ elliptic curve

Published on 11 Apr 2026 - 18:20

score 287 · Answer 4 · 2026-04-14 08:57:56

287

Views

Bounding Fundamental Units

Published on 14 Apr 2026 - 8:57

score 228 · Answer 5 · 2026-04-13 04:27:03

228

Views

What is the trace of an integer of algebraic degree $1$?

Published on 13 Apr 2026 - 4:27

score 329 · Answer 6 · 2026-04-10 22:33:56

329

Views

Probability that an irreducible polynomial has a root modulo a prime $p$

Published on 10 Apr 2026 - 22:33

score 221 · Answer 7 · 2026-04-09 01:15:52

221

Views

Brauer Group for a Global Field with $l$-roots of unity $l\neq \text{char}(F)$

Published on 09 Apr 2026 - 1:15

score 328 · Answer 8 · 2019-02-04 20:51:40

328

Views

For a number field $K$, does there exist totally splitting prime?

Published on 04 Feb 2019 - 20:51

score 147 · Answer 9 · 2026-04-13 23:46:19

147

Views

Why is there no equality in Krasner's lemma?

Published on 13 Apr 2026 - 23:46

score 666 · Answer 10 · 2026-03-25 15:39:48

666

Views

Algebraic independence and $\overline{\mathbb{Q}}-$ linear independence

Published on 25 Mar 2026 - 15:39

score 218 · Answer 11 · 2026-04-14 00:55:20

218

Views

Show that $\{1, \alpha, \alpha^2, \alpha^3\}$ is an integral basis in $k$, ( i.e. show that $\mathcal{O}_k = \Bbb{Z}[\alpha]$.)

Published on 14 Apr 2026 - 0:55

score 108 · Answer 12 · 2026-04-13 11:01:39

108

Views

$p$-adic power series and its maximum in the unit ball

Published on 13 Apr 2026 - 11:01

score 50 · Answer 13 · 2026-04-09 06:20:39

50

Views

Show that $S^p = \sum\limits_{x \in \Bbb {F_q}^*} \left ( \frac x q \right ) {\omega}^{xp}.$

Published on 09 Apr 2026 - 6:20

score 589 · Answer 14 · 2026-03-25 01:26:15

589

Views

What is the tensor product $\mathcal{O}_K \otimes_\mathbb{Q} \mathbb{R}$?

Published on 25 Mar 2026 - 1:26

score 63 · Answer 15 · 2026-04-09 08:09:18

63

Views

What is the reason for taking $\omega$ to be a primitive $q$-th root unity rather than taking any $q$-th root of unity?

Published on 09 Apr 2026 - 8:09

List Question

How to prove that one of $2,3,6$ is a square modulo every prime $p$?

Hasse's classification of Quaternion algebras (over number fields)

Commutativity of $End(E)$ for $E$ elliptic curve

Bounding Fundamental Units

What is the trace of an integer of algebraic degree $1$?

Probability that an irreducible polynomial has a root modulo a prime $p$

Brauer Group for a Global Field with $l$-roots of unity $l\neq \text{char}(F)$

For a number field $K$, does there exist totally splitting prime?

Why is there no equality in Krasner's lemma?

Algebraic independence and $\overline{\mathbb{Q}}-$ linear independence

Show that $\{1, \alpha, \alpha^2, \alpha^3\}$ is an integral basis in $k$, ( i.e. show that $\mathcal{O}_k = \Bbb{Z}[\alpha]$.)

$p$-adic power series and its maximum in the unit ball

Show that $S^p = \sum\limits_{x \in \Bbb {F_q}^*} \left ( \frac x q \right ) {\omega}^{xp}.$

What is the tensor product $\mathcal{O}_K \otimes_\mathbb{Q} \mathbb{R}$?

What is the reason for taking $\omega$ to be a primitive $q$-th root unity rather than taking any $q$-th root of unity?

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