Question

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

score 880 · Answer 1 · 2026-04-14 17:53:46

880

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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 14 Apr 2026 - 17:53

score 443 · Answer 2 · 2026-03-25 23:39:36

443

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

Published on 25 Mar 2026 - 23:39

score 3.7k · Answer 3 · 2026-03-25 23:37:13

3.7k

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Proving summations involving the Legendre symbol

Published on 25 Mar 2026 - 23:37

score 134 · Answer 4 · 2026-05-11 03:17:39

134

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Different formulations of the Law of Quadratic Reciprocity

Published on 11 May 2026 - 3:17

score 642 · Answer 5 · 2026-03-25 23:38:17

642

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

Published on 25 Mar 2026 - 23:38

score 261 · Answer 6 · 2026-03-25 22:06:38

261

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

Published on 25 Mar 2026 - 22:06

score 1.1k · Answer 7 · 2026-03-25 22:05:59

1.1k

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

Published on 25 Mar 2026 - 22:05

score 535 · Answer 8 · 2026-05-11 01:53:12

535

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

Published on 11 May 2026 - 1:53

score 1k · Answer 9 · 2026-05-10 14:26:45

1k

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Find pseudo-square mod $n$

Published on 10 May 2026 - 14:26

score 650 · Answer 10 · 2026-05-11 03:17:33

650

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

Published on 11 May 2026 - 3:17

score 4.8k · Answer 11 · 2026-03-25 23:39:11

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 25 Mar 2026 - 23:39

score 160 · Answer 12 · 2026-03-25 23:42:26

160

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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 25 Mar 2026 - 23:42

score 188 · Answer 13 · 2026-03-26 01:01:45

188

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Legendre Symbol confusion

Published on 26 Mar 2026 - 1:01

score 1.1k · Answer 14 · 2026-03-25 23:37:14

1.1k

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

Published on 25 Mar 2026 - 23:37

score 522 · Answer 15 · 2026-03-25 23:42:15

522

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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 25 Mar 2026 - 23:42

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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