Question

Is there any way to predict the largest number of consecutive quadratic or cubic residues modulo prime $p$?

score 225 · Answer 1 · 2026-03-25 14:25:35

225

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Is there any way to predict the largest number of consecutive quadratic or cubic residues modulo prime $p$?

Published on 25 Mar 2026 - 14:25

score 42 · Answer 2 · 2022-08-19 08:34:06

42

Views

What is the number of quadratic residues in $Z_{11^4}$?

Published on 19 Aug 2022 - 8:34

score 28 · Answer 3 · 2022-08-27 00:15:16

28

Views

Because it is enough to calculate these values to find the quadratic residue $x^2 ≡ a (mod 13)$

Published on 27 Aug 2022 - 0:15

score 75 · Answer 4 · 2022-09-07 11:38:14

75

Views

solve diophantine equation $a+b+2ab=n$

Published on 07 Sep 2022 - 11:38

score 33 · Answer 5 · 2026-02-23 13:46:13

33

Views

Quadratic residues and their using in proving the Édouard Lucas theorem related to Fermat numbers.

Published on 23 Feb 2026 - 13:46

score 123 · Answer 6 · 2022-09-14 20:20:09

123

Views

If $p$ is a prime where $p=4k+3$ and $a$ is a quadratic residue modulo $p$, then exactly one if its roots is a QR modulo $p$?

Published on 14 Sep 2022 - 20:20

score 751 · Answer 7 · 2022-09-25 21:43:00

751

Views

A primitive root modulo p is a primitive root modulo $p^2$ if and only if $g^{p-1} \not\equiv 1 \mod{p^2}$

Published on 25 Sep 2022 - 21:43

score 165 · Answer 8 · 2022-10-01 15:51:15

165

Views

Quadratic residues modulo pq

Published on 01 Oct 2022 - 15:51

score 46 · Answer 9 · 2026-03-26 14:34:38

46

Views

Missing link in Wikipedia's proof of quadratic reciprocity law

Published on 26 Mar 2026 - 14:34

score 118 · Answer 10 · 2026-03-29 22:13:27

118

Views

finding if a number $a$ is a quadratic residue mod $p$ computationally

Published on 29 Mar 2026 - 22:13

score 53 · Answer 11 · 2022-10-17 16:34:56

53

Views

The number of $x$ for which $-4x$ and $-4x+1$ are quadratic residues mod some odd prime number

Published on 17 Oct 2022 - 16:34

score 123 · Answer 12 · 2026-03-26 16:26:25

123

Views

Find all primes $p$ such that $ 3x^2-1\equiv 0 \mod{p}$ has a solution

Published on 26 Mar 2026 - 16:26

score 142 · Answer 13 · 2026-03-28 13:21:26

142

Views

Prove that $\sum_{y=0}^{p-1}\left(\frac{y}{p}\right)\left(\frac{y+d}{p}\right)=-1$

Published on 28 Mar 2026 - 13:21

score 250 · Answer 14 · 2022-10-29 13:15:37

250

Views

An interesting Legendre symbol identity: $\left (\frac{a}{p} \right ) = \prod_{h\in\mathscr{H}}^{}\frac{\sin(2\pi ah/p)}{\sin(2\pi h/p)}$

Published on 29 Oct 2022 - 13:15

score 96 · Answer 15 · 2022-11-07 14:11:24

96

Views

How to compute product of Jacobi symbols

Published on 07 Nov 2022 - 14:11

List Question

Is there any way to predict the largest number of consecutive quadratic or cubic residues modulo prime $p$?

What is the number of quadratic residues in $Z_{11^4}$?

Because it is enough to calculate these values to find the quadratic residue $x^2 ≡ a (mod 13)$

solve diophantine equation $a+b+2ab=n$

Quadratic residues and their using in proving the Édouard Lucas theorem related to Fermat numbers.

If $p$ is a prime where $p=4k+3$ and $a$ is a quadratic residue modulo $p$, then exactly one if its roots is a QR modulo $p$?

A primitive root modulo p is a primitive root modulo $p^2$ if and only if $g^{p-1} \not\equiv 1 \mod{p^2}$

Quadratic residues modulo pq

Missing link in Wikipedia's proof of quadratic reciprocity law

finding if a number $a$ is a quadratic residue mod $p$ computationally

The number of $x$ for which $-4x$ and $-4x+1$ are quadratic residues mod some odd prime number

Find all primes $p$ such that $ 3x^2-1\equiv 0 \mod{p}$ has a solution

Prove that $\sum_{y=0}^{p-1}\left(\frac{y}{p}\right)\left(\frac{y+d}{p}\right)=-1$

An interesting Legendre symbol identity: $\left (\frac{a}{p} \right ) = \prod_{h\in\mathscr{H}}^{}\frac{\sin(2\pi ah/p)}{\sin(2\pi h/p)}$

How to compute product of Jacobi symbols

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