Question

Prove $\sum\limits_{j=1}^{p-1} j\left(\frac{j}{p}\right) = 0 $ for an odd prime $p$ with $p\equiv 1\text{ mod } 4$

score 695 · Answer 1 · 2026-03-23 03:05:07

695

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Prove $\sum\limits_{j=1}^{p-1} j\left(\frac{j}{p}\right) = 0 $ for an odd prime $p$ with $p\equiv 1\text{ mod } 4$

Published on 23 Mar 2026 - 3:05

score 63 · Answer 2 · 2026-03-22 14:04:09

63

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Elementary Number Theory: Quadratic Reciprocity

Published on 22 Mar 2026 - 14:04

score 71 · Answer 3 · 2026-03-25 04:03:10

71

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Prove that there exists a number $x$ such that $x^2 \equiv 2$ (mod $p$) and $x^2 \equiv 3$ (mod $q$)

Published on 25 Mar 2026 - 4:03

score 191 · Answer 4 · 2026-03-16 23:05:45

191

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Use quadratic reciprocity to decide whether the following congruences are solvable

Published on 16 Mar 2026 - 23:05

score 186 · Answer 5 · 2026-03-17 05:53:36

186

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$3$ is a quadratic residue $\bmod p$ iff $ p \equiv \pm 1 \bmod12$

Published on 17 Mar 2026 - 5:53

score 155 · Answer 6 · 2026-03-22 08:31:21

155

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Quadratic Reciprocity problem.. help!

Published on 22 Mar 2026 - 8:31

score 1.6k · Answer 7 · 2026-03-17 11:59:43

1.6k

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Find the set of primes $p$ which $6$ is a quadratic residue $\mod p$

Published on 17 Mar 2026 - 11:59

score 298 · Answer 8 · 2026-03-22 01:44:40

298

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Condition for Quintic Reciprocity

Published on 22 Mar 2026 - 1:44

score 394 · Answer 9 · 2026-03-17 04:26:28

394

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Prove that $\forall x\in\mathbb{N}\ \text{ there always exists a prime }p\equiv1 \pmod 6 \text{ s.t. }p|(2x)^2+3;$

Published on 17 Mar 2026 - 4:26

score 107 · Answer 10 · 2026-03-25 05:36:29

107

Views

Diophantine equations for septic $(7$th$)$ power reciprocity

Published on 25 Mar 2026 - 5:36

score 217 · Answer 11 · 2026-03-17 05:39:26

217

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Writting Legendre Symbol as an element of group cohomology of $\mathbb{Q}$

Published on 17 Mar 2026 - 5:39

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

401

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

Published on 25 Mar 2026 - 4:42

score 367 · Answer 13 · 2026-03-25 03:01:23

367

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Solutions to $x^2+x-1\equiv 0$ mod $p$

Published on 25 Mar 2026 - 3:01

score 202 · Answer 14 · 2026-03-25 03:07:34

202

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if $19a^2 \equiv b^2 \pmod 7$ then $19a^2 \equiv b^2 \pmod {7^2}$

Published on 25 Mar 2026 - 3:07

score 133 · Answer 15 · 2026-03-25 03:00:32

133

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Proof that $x^4 - qy^4 = az^2$ has no integral solution

Published on 25 Mar 2026 - 3:00

List Question

Prove $\sum\limits_{j=1}^{p-1} j\left(\frac{j}{p}\right) = 0 $ for an odd prime $p$ with $p\equiv 1\text{ mod } 4$

Elementary Number Theory: Quadratic Reciprocity

Prove that there exists a number $x$ such that $x^2 \equiv 2$ (mod $p$) and $x^2 \equiv 3$ (mod $q$)

Use quadratic reciprocity to decide whether the following congruences are solvable

$3$ is a quadratic residue $\bmod p$ iff $ p \equiv \pm 1 \bmod12$

Quadratic Reciprocity problem.. help!

Find the set of primes $p$ which $6$ is a quadratic residue $\mod p$

Condition for Quintic Reciprocity

Prove that $\forall x\in\mathbb{N}\ \text{ there always exists a prime }p\equiv1 \pmod 6 \text{ s.t. }p|(2x)^2+3;$

Diophantine equations for septic $(7$th$)$ power reciprocity

Writting Legendre Symbol as an element of group cohomology of $\mathbb{Q}$

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

Solutions to $x^2+x-1\equiv 0$ mod $p$

if $19a^2 \equiv b^2 \pmod 7$ then $19a^2 \equiv b^2 \pmod {7^2}$

Proof that $x^4 - qy^4 = az^2$ has no integral solution

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