List questions from quadratic-residues

Published on 20 Apr 2023 - 22:21

77

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Legendre symbol on $p$-adic integers $\mathbb{Z}_p$

Published on 23 Apr 2023 - 7:02

71

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Show that $z^2$ is a fourth power mod $q$ if and only if $\left(\frac{z}{q}\right) = 1$, given that $q \equiv 1 \pmod{4}$.

Published on 25 Mar 2026 - 14:35

131

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Find the number of integer solutions of $22x^2-34xy+6y^2=2024$

Published on 17 May 2023 - 15:56

96

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How to prove that primes congruent to $\pm1$ mod $5$ are of the form $5 a^2 - b^2$

Published on 22 May 2023 - 22:34

42

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Given $y$, is $-\left(\dfrac{x - y}{2}\right)^2$ is a quadratic residue $\pmod x$?

Published on 12 Jun 2023 - 19:09

56

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Help with summing characters

Published on 22 Mar 2026 - 7:20

97

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Quadratic residues that are also squares themselves

Published on 18 Jun 2023 - 14:12

91

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How to find the square root of an element in an abelian group of even order?

Published on 06 Jul 2023 - 19:15

132

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Legendre symbols always match?

Published on 14 Jul 2023 - 14:58

59

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Stuck in a quadratic reciprocity problem

Published on 25 Mar 2026 - 14:29

126

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Cardinality of set of quadratic residue of mod n.

Published on 10 Aug 2023 - 18:25

39

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Sequences in finite fields producing quadratic residues

Published on 16 Aug 2023 - 17:14

248

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Is the quadratic residue the only restriction?

Published on 25 Mar 2026 - 10:55

88

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Where did Euler publish his formular for the Legendre Symbol?

Published on 20 Sep 2023 - 9:24

List Question

(103/1009) Evaluate The Legendre Symbol

Legendre symbol on $p$-adic integers $\mathbb{Z}_p$

Show that $z^2$ is a fourth power mod $q$ if and only if $\left(\frac{z}{q}\right) = 1$, given that $q \equiv 1 \pmod{4}$.

Find the number of integer solutions of $22x^2-34xy+6y^2=2024$

How to prove that primes congruent to $\pm1$ mod $5$ are of the form $5 a^2 - b^2$

Given $y$, is $-\left(\dfrac{x - y}{2}\right)^2$ is a quadratic residue $\pmod x$?

Help with summing characters

Quadratic residues that are also squares themselves

How to find the square root of an element in an abelian group of even order?

Legendre symbols always match?

Stuck in a quadratic reciprocity problem

Cardinality of set of quadratic residue of mod n.

Sequences in finite fields producing quadratic residues

Is the quadratic residue the only restriction?

Where did Euler publish his formular for the Legendre Symbol?

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