Question

How to prove this summation involving Legendre symbol: $\sum\limits_{k=1}^{p-1}k\left(\frac{k}{p}\right)=0 $

score 878 · Answer 1 · 2017-04-05 22:49:03

878

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How to prove this summation involving Legendre symbol: $\sum\limits_{k=1}^{p-1}k\left(\frac{k}{p}\right)=0 $

Published on 05 Apr 2017 - 22:49

score 442 · Answer 2 · 2015-04-08 02:32:08

442

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Legendre Symbol $\left(\frac4p\right)$ is always congruent to $1$?

Published on 08 Apr 2015 - 2:32

score 3.7k · Answer 3 · 2015-04-08 22:27:47

3.7k

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Proving summations involving the Legendre symbol

Published on 08 Apr 2015 - 22:27

score 133 · Answer 4 · 2026-03-25 16:13:54

133

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Different formulations of the Law of Quadratic Reciprocity

Published on 25 Mar 2026 - 16:13

score 641 · Answer 5 · 2015-04-30 05:18:19

641

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Legendre Symbol $\left ( \frac{7}{p} \right ) = \left ( \frac{7}{q} \right )$

Published on 30 Apr 2015 - 5:18

score 260 · Answer 6 · 2015-05-04 13:33:10

260

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Why is $\sum_{x=1}^{p-1}\left(\frac{x}{p}\right)=\left(\frac{0}{p}\right)$?

Published on 04 May 2015 - 13:33

score 1.1k · Answer 7 · 2015-05-04 15:37:07

1.1k

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Find the set of primes p for which -3 is quadratic residue mod p

Published on 04 May 2015 - 15:37

score 534 · Answer 8 · 2026-03-25 16:20:54

534

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Calculating the Legendre symbols $\left(\frac{295}{401}\right)$ and $\left(\frac{713}{1009}\right)$ using quadratic reciprocity

Published on 25 Mar 2026 - 16:20

score 1k · Answer 9 · 2026-02-23 04:34:43

1k

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Find pseudo-square mod $n$

Published on 23 Feb 2026 - 4:34

score 649 · Answer 10 · 2026-03-25 16:13:49

649

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Describe the set of odd primes such that $\left(\frac{-5}{p}\right) = 1$ (Legendre Symbol)

Published on 25 Mar 2026 - 16:13

score 4.8k · Answer 11 · 2015-05-09 02:16:34

4.8k

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When $p=3 \pmod 4$, show that $a^{(p+1)/4} \pmod p$ is a square root of $a$

Published on 09 May 2015 - 2:16

score 159 · Answer 12 · 2015-05-12 00:54:04

159

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Use Gauss' Lemma to find Legendre symbol $\left(\frac{-1}{n}\right)$ for $n \equiv 1, 3, 5, 7 \pmod 8$.

Published on 12 May 2015 - 0:54

score 187 · Answer 13 · 2015-05-13 12:46:10

187

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Legendre Symbol confusion

Published on 13 May 2015 - 12:46

score 1.1k · Answer 14 · 2015-05-18 02:14:45

1.1k

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For which primes is $-2$ a quadratic residue?

Published on 18 May 2015 - 2:14

score 521 · Answer 15 · 2015-05-18 03:32:33

521

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the number of solutions of the congruence $x^2 \equiv a \pmod m$ is $\prod_{p \mid m} \left(1+ \left(\dfrac{a}{p} \right) \right).$

Published on 18 May 2015 - 3:32

List Question

How to prove this summation involving Legendre symbol: $\sum\limits_{k=1}^{p-1}k\left(\frac{k}{p}\right)=0 $

Legendre Symbol $\left(\frac4p\right)$ is always congruent to $1$?

Proving summations involving the Legendre symbol

Different formulations of the Law of Quadratic Reciprocity

Legendre Symbol $\left ( \frac{7}{p} \right ) = \left ( \frac{7}{q} \right )$

Why is $\sum_{x=1}^{p-1}\left(\frac{x}{p}\right)=\left(\frac{0}{p}\right)$?

Find the set of primes p for which -3 is quadratic residue mod p

Calculating the Legendre symbols $\left(\frac{295}{401}\right)$ and $\left(\frac{713}{1009}\right)$ using quadratic reciprocity

Find pseudo-square mod $n$

Describe the set of odd primes such that $\left(\frac{-5}{p}\right) = 1$ (Legendre Symbol)

When $p=3 \pmod 4$, show that $a^{(p+1)/4} \pmod p$ is a square root of $a$

Use Gauss' Lemma to find Legendre symbol $\left(\frac{-1}{n}\right)$ for $n \equiv 1, 3, 5, 7 \pmod 8$.

Legendre Symbol confusion

For which primes is $-2$ a quadratic residue?

the number of solutions of the congruence $x^2 \equiv a \pmod m$ is $\prod_{p \mid m} \left(1+ \left(\dfrac{a}{p} \right) \right).$

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