Question

Determine if $-42$ is a quadratic residue of $\pmod{61}$

score 289 · Answer 1 · 2014-04-21 22:05:44

289

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Determine if $-42$ is a quadratic residue of $\pmod{61}$

Published on 21 Apr 2014 - 22:05

score 606 · Answer 2 · 2026-03-25 07:40:41

606

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Is every integer a quadratic residue mod some p?

Published on 25 Mar 2026 - 7:40

score 979 · Answer 3 · 2026-03-25 20:12:43

979

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Using Wilson's theorem, show that if $p$ is prime of the form $p=4n+1$ and if $y=(\frac {p-1}2)!$, then $y^2\equiv -1\mod p$.

Published on 25 Mar 2026 - 20:12

score 64 · Answer 4 · 2014-05-05 20:38:04

64

Views

Show that for any integer $n=1,..,32$ such that $(n,33) = 1$, $\left(\frac{n}{33}\right) = \left(\frac{33-n}{33}\right)$

Published on 05 May 2014 - 20:38

score 980 · Answer 5 · 2026-03-25 11:06:24

980

Views

finding all primes $p$ for which a given number is a quadratic residue

Published on 25 Mar 2026 - 11:06

score 298 · Answer 6 · 2026-03-25 14:06:55

298

Views

Help for solving quadratic residue.

Published on 25 Mar 2026 - 14:06

score 607 · Answer 7 · 2026-03-25 14:25:40

607

Views

A combinatorial proof of Euler's Criterion? $(\tfrac{a}{p})\equiv a^{\frac{p-1}{2}} \text{ mod p}$

Published on 25 Mar 2026 - 14:25

score 555 · Answer 8 · 2014-05-31 07:10:04

555

Views

Quadratic residue modulo $p$ iff quadratic residue module $p^k$

Published on 31 May 2014 - 7:10

score 82 · Answer 9 · 2014-06-06 07:48:08

82

Views

A question about squares

Published on 06 Jun 2014 - 7:48

score 2.6k · Answer 10 · 2026-03-25 07:46:20

2.6k

Views

Find the value of the following Legendre Symbols and Use Gausslemma to compute each of the Legendre symbols below

Published on 25 Mar 2026 - 7:46

score 379 · Answer 11 · 2026-03-25 11:13:39

379

Views

Elementary, direct proof of when $5$ is a quadratic residue mod $p$

Published on 25 Mar 2026 - 11:13

score 83 · Answer 12 · 2014-07-22 13:46:17

83

Views

Proving $\frac{p-1}{2}!\equiv (-1)^t$ where $t$ is the number of integers which are not quadratic squares

Published on 22 Jul 2014 - 13:46

score 690 · Answer 13 · 2014-07-28 10:49:17

690

Views

When does -1 have a squareroot in a finite field? (-1 as a quadratic residue)

Published on 28 Jul 2014 - 10:49

score 90 · Answer 14 · 2014-07-29 03:48:57

90

Views

Quadratic Residues in $\mathbb{Z}/3^n \mathbb{Z} $

Published on 29 Jul 2014 - 3:48

score 218 · Answer 15 · 2026-03-25 07:49:17

218

Views

Exercise of Quadratic Reciprocity

Published on 25 Mar 2026 - 7:49

List Question

Determine if $-42$ is a quadratic residue of $\pmod{61}$

Is every integer a quadratic residue mod some p?

Using Wilson's theorem, show that if $p$ is prime of the form $p=4n+1$ and if $y=(\frac {p-1}2)!$, then $y^2\equiv -1\mod p$.

Show that for any integer $n=1,..,32$ such that $(n,33) = 1$, $\left(\frac{n}{33}\right) = \left(\frac{33-n}{33}\right)$

finding all primes $p$ for which a given number is a quadratic residue

Help for solving quadratic residue.

A combinatorial proof of Euler's Criterion? $(\tfrac{a}{p})\equiv a^{\frac{p-1}{2}} \text{ mod p}$

Quadratic residue modulo $p$ iff quadratic residue module $p^k$

A question about squares

Find the value of the following Legendre Symbols and Use Gausslemma to compute each of the Legendre symbols below

Elementary, direct proof of when $5$ is a quadratic residue mod $p$

Proving $\frac{p-1}{2}!\equiv (-1)^t$ where $t$ is the number of integers which are not quadratic squares

When does -1 have a squareroot in a finite field? (-1 as a quadratic residue)

Quadratic Residues in $\mathbb{Z}/3^n \mathbb{Z} $

Exercise of Quadratic Reciprocity

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