List questions from quadratic-reciprocity

Published on 19 May 2015 - 18:53

280

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What is the probability of having a quadratic residue?

Published on 16 Jun 2015 - 12:16

741

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Verifying quadratic reciprocity for the Jacobi symbol

Published on 19 Jun 2015 - 16:07

49

Views

Quadratic reciprocity in the case $a=-1$

Published on 29 Jul 2015 - 20:58

65

Views

Technological incompetence

Published on 19 Aug 2015 - 19:19

213

Views

Gauss' original proof of quadratic reciprocity

Published on 31 Aug 2015 - 19:52

56

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Missing link in proof of quadratic reciprocity law

Published on 13 Sep 2015 - 9:44

91

Views

verify if $8x^2 - 2x - 3 \equiv 0 \pmod{75}$ has solutions or not.

Published on 10 Oct 2015 - 11:01

136

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Prove that $\sum^{P}_{k=1} \lfloor\frac {ka}{p}\rfloor = \frac{p^{2} - 1}{8} + \mu(a,p)$ mod$(2)$

Published on 24 Mar 2026 - 15:37

359

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If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.

Published on 27 Oct 2015 - 6:32

163

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Let $p> 7$, prove that $\left(\frac{2}{q}\right) = (-1)^{\frac{q^2-1}{8}}$ with $q$ an odd prime

Published on 28 Oct 2015 - 22:33

275

Views

Irreducibility in a polynomial related to quadratic residues

Published on 29 Nov 2015 - 14:44

49

Views

Quadratic congruence with linear term

Published on 23 Mar 2026 - 0:31

442

Views

If $p>3$ and $x^2+3y^2=p$, prove $\left(\frac{-3}{p}\right)=1$ and $p\equiv 1\pmod{6}$.

Published on 07 Mar 2026 - 11:06

232

Views

Quadratic Reciprocity and Congruences

Published on 24 Mar 2026 - 2:38

List Question

Describe all odd primes p for which 7 is a quadratic residue

What is the probability of having a quadratic residue?

Verifying quadratic reciprocity for the Jacobi symbol

Quadratic reciprocity in the case $a=-1$

Technological incompetence

Gauss' original proof of quadratic reciprocity

Missing link in proof of quadratic reciprocity law

verify if $8x^2 - 2x - 3 \equiv 0 \pmod{75}$ has solutions or not.

Prove that $\sum^{P}_{k=1} \lfloor\frac {ka}{p}\rfloor = \frac{p^{2} - 1}{8} + \mu(a,p)$ mod$(2)$

If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.

Let $p> 7$, prove that $\left(\frac{2}{q}\right) = (-1)^{\frac{q^2-1}{8}}$ with $q$ an odd prime

Irreducibility in a polynomial related to quadratic residues

Quadratic congruence with linear term

If $p>3$ and $x^2+3y^2=p$, prove $\left(\frac{-3}{p}\right)=1$ and $p\equiv 1\pmod{6}$.

Quadratic Reciprocity and Congruences

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