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A question about Legendre symbols

score 62 · Answer 1 · 2023-09-27 17:53:50

62

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A question about Legendre symbols

Published on 27 Sep 2023 - 17:53

score 71 · Answer 2 · 2023-10-09 23:18:56

71

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$\sum _{r=1}^{p-1}r^{2k}\left(\frac{r}{p}\right)=\sum_{i=1}^{2k-1} c_i(p)\sum _{r=1}^{p-1}r^{2k-i}\left(\frac{r}{p}\right)$

Published on 09 Oct 2023 - 23:18

score 33 · Answer 3 · 2023-10-10 09:29:59

33

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The distribution of which numbers have square roots in $\mathbb Z_p$ and how many

Published on 10 Oct 2023 - 9:29

score 145 · Answer 4 · 2023-10-20 17:44:10

145

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how to find p-th primitive root of unity in GF(2^m)

Published on 20 Oct 2023 - 17:44

score 58 · Answer 5 · 2023-10-23 22:30:56

58

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Prove that if $n$ is odd and $p \mid n$, then $\sum_{m=1,\, \gcd(m,n)=1}^{\varphi(n)} (\frac{m}{p})=0$

Published on 23 Oct 2023 - 22:30

score 56 · Answer 6 · 2023-10-28 04:02:07

56

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Residual theorem for ellipse perimeter integral

Published on 28 Oct 2023 - 4:02

score 35 · Answer 7 · 2023-11-07 21:24:19

35

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Prove that there exists $1\leq a < p^{1/(2\sqrt{e})} (\log p)^2$ that is a quadratic non-residue modulo p

Published on 07 Nov 2023 - 21:24

score 38 · Answer 8 · 2023-11-09 15:08:17

38

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Find a criterion for the odd primes p for which the congruence $x^2 + x + 3 \equiv 0 \pmod p$ has at least one solution.

Published on 09 Nov 2023 - 15:08

score 10 · Answer 9 · 2026-03-10 21:35:05

10

Views

How to recognize anisotropic quaternary rational quadratic forms?

Published on 10 Mar 2026 - 21:35

score 39 · Answer 10 · 2023-11-14 10:27:16

39

Views

Quadratic Residue for even numbers?

Published on 14 Nov 2023 - 10:27

score 99 · Answer 11 · 2023-11-15 18:07:18

99

Views

Experimentally found weird number theory pattern $p^\frac{d-3}{2}\cdot \left(p^\frac{d-1}2 \pm \{-1 \text{ or } p-1 \}\right) \mod d$ equals $0,1$

Published on 15 Nov 2023 - 18:07

score 77 · Answer 12 · 2023-11-16 10:53:55

77

Views

The least quadratic non-residue

Published on 16 Nov 2023 - 10:53

score 104 · Answer 13 · 2023-11-22 14:09:50

104

Views

Principal square root of quadratic residue mod $n$, where $n$ is a Blum integer

Published on 22 Nov 2023 - 14:09

score 73 · Answer 14 · 2026-03-26 01:02:05

73

Views

A Diophantine equation centered around the divisor counting function and squares

Published on 26 Mar 2026 - 1:02

score 143 · Answer 15 · 2023-12-13 16:54:14

143

Views

Is there any solution to $x^2 \equiv 53 \mod97$

Published on 13 Dec 2023 - 16:54

List Question

A question about Legendre symbols

$\sum _{r=1}^{p-1}r^{2k}\left(\frac{r}{p}\right)=\sum_{i=1}^{2k-1} c_i(p)\sum _{r=1}^{p-1}r^{2k-i}\left(\frac{r}{p}\right)$

The distribution of which numbers have square roots in $\mathbb Z_p$ and how many

how to find p-th primitive root of unity in GF(2^m)

Prove that if $n$ is odd and $p \mid n$, then $\sum_{m=1,\, \gcd(m,n)=1}^{\varphi(n)} (\frac{m}{p})=0$

Residual theorem for ellipse perimeter integral

Prove that there exists $1\leq a < p^{1/(2\sqrt{e})} (\log p)^2$ that is a quadratic non-residue modulo p

Find a criterion for the odd primes p for which the congruence $x^2 + x + 3 \equiv 0 \pmod p$ has at least one solution.

How to recognize anisotropic quaternary rational quadratic forms?

Quadratic Residue for even numbers?

Experimentally found weird number theory pattern $p^\frac{d-3}{2}\cdot \left(p^\frac{d-1}2 \pm \{-1 \text{ or } p-1 \}\right) \mod d$ equals $0,1$

The least quadratic non-residue

Principal square root of quadratic residue mod $n$, where $n$ is a Blum integer

A Diophantine equation centered around the divisor counting function and squares

Is there any solution to $x^2 \equiv 53 \mod97$

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