List questions from legendre-symbol

Published on 25 Mar 2026 - 12:53

105

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

Published on 25 Mar 2026 - 12:53

99

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

Published on 10 May 2026 - 17:16

278

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

Published on 10 May 2026 - 17:16

63

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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 15 Apr 2026 - 18:11

47

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Consequences of Jacobi and Legendre Symbols

Published on 05 May 2026 - 13:36

53

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

Published on 16 Apr 2026 - 10:33

190

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Number of values such that quadratic residue is 1

Published on 17 Apr 2026 - 3:35

1.9k

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

Published on 16 Apr 2026 - 10:55

609

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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 16 Apr 2026 - 7:21

542

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

Published on 11 Apr 2026 - 14:07

112

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

Published on 25 Mar 2026 - 12:54

34

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

Published on 25 Mar 2026 - 14:26

28

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

Published on 25 Mar 2026 - 12:54

54

Views

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

Published on 25 Mar 2026 - 16:02

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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