Question

$X^2 + Y^2 \equiv 0 \pmod p$ implies that $-1$ is a square in $\mathbb{Z}/p\mathbb{Z}$

score 46 · Answer 1 · 2020-12-08 16:58:45

46

Views

$X^2 + Y^2 \equiv 0 \pmod p$ implies that $-1$ is a square in $\mathbb{Z}/p\mathbb{Z}$

Published on 08 Dec 2020 - 16:58

score 175 · Answer 2 · 2020-12-27 02:20:03

175

Views

Proving that if $a$ is not a quadratic residue, then $a^{p'}\equiv -1\pmod p$: Is my proof correct?

Published on 27 Dec 2020 - 2:20

score 153 · Answer 3 · 2020-12-27 23:03:08

153

Views

Solving Equation of form: num = $x^3 + ax^2 + bx + c$.

Published on 27 Dec 2020 - 23:03

score 214 · Answer 4 · 2020-12-30 08:50:25

214

Views

$24ml+1=k^2$ has no solution for all $l=1 \dots m$

Published on 30 Dec 2020 - 8:50

score 84 · Answer 5 · 2026-03-26 11:24:21

84

Views

Gaussian sets modulo $p$.

Published on 26 Mar 2026 - 11:24

score 121 · Answer 6 · 2021-01-02 15:30:56

121

Views

Find all $f(X)\in\mathbb{Z}[X]$ such that $\left(\frac{f(n)}{p}\right)=\left(\frac{n}{p}\right)$ [Legendre symbol and $p$ is a fixed prime]

Published on 02 Jan 2021 - 15:30

score 685 · Answer 7 · 2026-02-23 12:08:47

685

Views

Showing that $p$ is a Fermat prime if and only if every quadratic non-residue mod $p$ is also a primitive root mod $p$

Published on 23 Feb 2026 - 12:08

score 179 · Answer 8 · 2026-03-26 17:53:31

179

Views

Proof of $n$ being quadratic residue for primes of the form $4n+1$

Published on 26 Mar 2026 - 17:53

score 174 · Answer 9 · 2021-01-12 08:15:12

174

Views

How to prove these pseudo-random number generators don't repeat until running through the entire set?

Published on 12 Jan 2021 - 8:15

score 77 · Answer 10 · 2021-01-19 05:21:14

77

Views

Binomial theorem and a congruence modulo $2^{2m+2}$

Published on 19 Jan 2021 - 5:21

score 69 · Answer 11 · 2021-01-22 06:23:34

69

Views

Using quadratic residue

Published on 22 Jan 2021 - 6:23

score 97 · Answer 12 · 2021-01-22 07:32:17

97

Views

Using Quadratic Residue to show that $2^m-1$ doesn't divide $3^n-1$

Published on 22 Jan 2021 - 7:32

score 546 · Answer 13 · 2021-01-24 10:39:49

546

Views

The sum of quadratic residues mod $p$ is $0$

Published on 24 Jan 2021 - 10:39

score 65 · Answer 14 · 2026-03-26 17:53:50

65

Views

Question about the Legendre's symbol: $\left(\frac{p-1}{5}\right) \overset?= \left(\frac{5}{p}\right)$

Published on 26 Mar 2026 - 17:53

score 415 · Answer 15 · 2021-02-16 22:05:13

415

Views

Solve $x^2 \equiv -1 \pmod{41} $

Published on 16 Feb 2021 - 22:05

List Question

$X^2 + Y^2 \equiv 0 \pmod p$ implies that $-1$ is a square in $\mathbb{Z}/p\mathbb{Z}$

Proving that if $a$ is not a quadratic residue, then $a^{p'}\equiv -1\pmod p$: Is my proof correct?

Solving Equation of form: num = $x^3 + ax^2 + bx + c$.

$24ml+1=k^2$ has no solution for all $l=1 \dots m$

Gaussian sets modulo $p$.

Find all $f(X)\in\mathbb{Z}[X]$ such that $\left(\frac{f(n)}{p}\right)=\left(\frac{n}{p}\right)$ [Legendre symbol and $p$ is a fixed prime]

Showing that $p$ is a Fermat prime if and only if every quadratic non-residue mod $p$ is also a primitive root mod $p$

Proof of $n$ being quadratic residue for primes of the form $4n+1$

How to prove these pseudo-random number generators don't repeat until running through the entire set?

Binomial theorem and a congruence modulo $2^{2m+2}$

Using quadratic residue

Using Quadratic Residue to show that $2^m-1$ doesn't divide $3^n-1$

The sum of quadratic residues mod $p$ is $0$

Question about the Legendre's symbol: $\left(\frac{p-1}{5}\right) \overset?= \left(\frac{5}{p}\right)$

Solve $x^2 \equiv -1 \pmod{41} $

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