List questions from legendre-symbol

Published on 20 Jul 2019 - 11:03

104

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How to determine $(\tfrac{-5}{p})$ $\mod 20$?

Published on 20 Jul 2019 - 11:37

98

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quadratic residue such as "$(n|p)= -1$"(quadratic reciprocity)

Published on 25 Mar 2026 - 9:28

277

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A prime number is not a quadratic residue modulo some prime without quadratic reciprocity

Published on 25 Mar 2026 - 9:28

60

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$(\frac{a}{p})=(\frac{b}{p})$ iff $\exists c: b\equiv\ c^2a\pmod p$ and $(c,p)=1$.

Published on 12 Sep 2019 - 4:07

43

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Consequences of Jacobi and Legendre Symbols

Published on 25 Mar 2026 - 4:52

50

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Existence of an integer $i$ such that $i$ and $i+1$ are both squares mod $p$

Published on 26 Sep 2019 - 13:50

187

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Number of values such that quadratic residue is 1

Published on 28 Sep 2019 - 17:02

1.9k

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Prove that Legendre Symbol $\left(\frac{(p-1)!}p\right) \equiv p\pmod4$

Published on 14 Apr 2014 - 0:14

606

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A combinatorial proof of Euler's Criterion? $(\tfrac{a}{p})\equiv a^{\frac{p-1}{2}} \text{ mod p}$

Published on 17 May 2014 - 21:17

539

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How can I prove the following properties of the Legendre-symbol?

Published on 03 Dec 2014 - 17:41

111

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Show that $(n^5-n+3)$ is not a perfect square

Published on 10 Oct 2019 - 9:15

33

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Legendre symbol for a prime of the form $m^2-dn^2$

Published on 11 Oct 2019 - 4:14

27

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lattice structure of a subset of $\Bbb Z^2$

Published on 11 Oct 2019 - 21:53

53

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Calculating Legendre symbol : $\left(\frac{3}{2^{2^n}+1}\right)$ , n being positive.

Published on 17 Oct 2019 - 2:32

List Question

Is there a quick way of using Gauss's lemma for large $p$?

How to determine $(\tfrac{-5}{p})$ $\mod 20$?

quadratic residue such as "$(n|p)= -1$"(quadratic reciprocity)

A prime number is not a quadratic residue modulo some prime without quadratic reciprocity

$(\frac{a}{p})=(\frac{b}{p})$ iff $\exists c: b\equiv\ c^2a\pmod p$ and $(c,p)=1$.

Consequences of Jacobi and Legendre Symbols

Existence of an integer $i$ such that $i$ and $i+1$ are both squares mod $p$

Number of values such that quadratic residue is 1

Prove that Legendre Symbol $\left(\frac{(p-1)!}p\right) \equiv p\pmod4$

A combinatorial proof of Euler's Criterion? $(\tfrac{a}{p})\equiv a^{\frac{p-1}{2}} \text{ mod p}$

How can I prove the following properties of the Legendre-symbol?

Show that $(n^5-n+3)$ is not a perfect square

Legendre symbol for a prime of the form $m^2-dn^2$

lattice structure of a subset of $\Bbb Z^2$

Calculating Legendre symbol : $\left(\frac{3}{2^{2^n}+1}\right)$ , n being positive.

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