Question

Showing that $\sum_{x \in \mathbb{F}_p} \left(\frac{x^2-1}{p}\right) = -1$, where $\left(\frac{x}{p}\right)$ is the Legendre symbol

score 242 · Answer 1 · 2018-10-02 18:33:02

242

Views

Showing that $\sum_{x \in \mathbb{F}_p} \left(\frac{x^2-1}{p}\right) = -1$, where $\left(\frac{x}{p}\right)$ is the Legendre symbol

Published on 02 Oct 2018 - 18:33

score 950 · Answer 2 · 2018-10-29 01:27:32

950

Views

Evaluate the Legendre symbol $(\frac{14}{p})$ for $p > 2$.

Published on 29 Oct 2018 - 1:27

score 231 · Answer 3 · 2018-10-30 10:02:20

231

Views

Let $p,q$ be odd primes such that $p-q=4a.$ Prove that $\Bigg(\dfrac{a}{p}\Bigg)=\Bigg(\dfrac{a}{q}\Bigg).$

Published on 30 Oct 2018 - 10:02

score 156 · Answer 4 · 2018-11-03 00:36:29

156

Views

The Number of involutory matrices over $\mathbb{Z_p} $

Published on 03 Nov 2018 - 0:36

score 740 · Answer 5 · 2018-11-05 08:28:22

740

Views

If $p \equiv 3 \ (\text{mod} \ 4)$ is a prime, show $(\frac{p-1}{2})! \equiv (-1)^{t} \ (\text{mod} \ p)$

Published on 05 Nov 2018 - 8:28

score 667 · Answer 6 · 2018-11-15 15:14:51

667

Views

Sum of Legendre symbol $\left(\frac{n^2-a}{p}\right)$ (More explanation)

Published on 15 Nov 2018 - 15:14

score 620 · Answer 7 · 2018-11-28 10:07:49

620

Views

Find p primes odds for Legendre symbol $(-3|p)=+1$ or $(-3|p)=-1$

Published on 28 Nov 2018 - 10:07

score 836 · Answer 8 · 2018-11-29 14:41:58

836

Views

Proof that $5$ is a quadratic residue $(\mod p)$ with $p$ odd prime iif $p \equiv \pm 1 \mod 10$

Published on 29 Nov 2018 - 14:41

score 148 · Answer 9 · 2018-12-01 05:07:04

148

Views

If $p=a^2+b^2$ prove these consequences about $\big(\!\frac{a}{p}\!\big)$

Published on 01 Dec 2018 - 5:07

score 408 · Answer 10 · 2018-12-05 10:19:09

408

Views

Determine the Legendre symbol of $\left(\frac{14}{p}\right)$

Published on 05 Dec 2018 - 10:19

score 1k · Answer 11 · 2018-12-06 08:40:16

1k

Views

Find all primes $p$ : $x^2 \equiv 13 \pmod p$ has solutions

Published on 06 Dec 2018 - 8:40

score 401 · Answer 12 · 2026-03-25 04:42:39

401

Views

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

Published on 25 Mar 2026 - 4:42

score 838 · Answer 13 · 2018-12-10 13:24:50

838

Views

Prove that there are infinitely many prime numbers $p$ such that $\left(\frac{a}{p}\right)=1$ for fixed $a$.

Published on 10 Dec 2018 - 13:24

score 708 · Answer 14 · 2018-12-12 08:05:20

708

Views

A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.

Published on 12 Dec 2018 - 8:05

score 353 · Answer 15 · 2018-12-12 12:16:44

353

Views

Proof that Legendre symbol $\Big(\frac{a}{p}\Big)$ is $a^{\frac{p-1}{2}}$

Published on 12 Dec 2018 - 12:16

List Question

Showing that $\sum_{x \in \mathbb{F}_p} \left(\frac{x^2-1}{p}\right) = -1$, where $\left(\frac{x}{p}\right)$ is the Legendre symbol

Evaluate the Legendre symbol $(\frac{14}{p})$ for $p > 2$.

Let $p,q$ be odd primes such that $p-q=4a.$ Prove that $\Bigg(\dfrac{a}{p}\Bigg)=\Bigg(\dfrac{a}{q}\Bigg).$

The Number of involutory matrices over $\mathbb{Z_p} $

If $p \equiv 3 \ (\text{mod} \ 4)$ is a prime, show $(\frac{p-1}{2})! \equiv (-1)^{t} \ (\text{mod} \ p)$

Sum of Legendre symbol $\left(\frac{n^2-a}{p}\right)$ (More explanation)

Find p primes odds for Legendre symbol $(-3|p)=+1$ or $(-3|p)=-1$

Proof that $5$ is a quadratic residue $(\mod p)$ with $p$ odd prime iif $p \equiv \pm 1 \mod 10$

If $p=a^2+b^2$ prove these consequences about $\big(\!\frac{a}{p}\!\big)$

Determine the Legendre symbol of $\left(\frac{14}{p}\right)$

Find all primes $p$ : $x^2 \equiv 13 \pmod p$ has solutions

What are the Legendre symbols $\left(\frac{10}{31}\right)$ and $\left(\frac{-15}{43}\right)$?

Prove that there are infinitely many prime numbers $p$ such that $\left(\frac{a}{p}\right)=1$ for fixed $a$.

A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.

Proof that Legendre symbol $\Big(\frac{a}{p}\Big)$ is $a^{\frac{p-1}{2}}$

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