Question

$\forall p \ge 11 \quad \exists n \in \{1,2,\dots,9\}$ such that $n$ and $n+1$ are quadratic residues mod p

score 45 · Answer 1 · 2019-06-19 09:26:40

45

Views

$\forall p \ge 11 \quad \exists n \in \{1,2,\dots,9\}$ such that $n$ and $n+1$ are quadratic residues mod p

Published on 19 Jun 2019 - 9:26

score 1.2k · Answer 2 · 2019-06-19 14:38:38

1.2k

Views

Solutions of $x^2 \equiv 1 \pmod N$

Published on 19 Jun 2019 - 14:38

score 370 · Answer 3 · 2019-06-20 16:10:32

370

Views

Show that a following equation has no solution in integers: $x^3-x+9=5y^2$

Published on 20 Jun 2019 - 16:10

score 1.2k · Answer 4 · 2019-06-23 13:59:55

1.2k

Views

Let $p$ be a prime of the form $p = a^2 + b^2$ with $a,b \in \mathbb{Z}$ and $a$ an odd prime. Prove that $(a/p) =1$

Published on 23 Jun 2019 - 13:59

score 79 · Answer 5 · 2019-06-23 15:08:46

79

Views

Show that a is a quadratic residue modulo $p$ iff $ind_{r} (\mathbb{a})$ is even.

Published on 23 Jun 2019 - 15:08

score 92 · Answer 6 · 2026-03-25 06:13:01

92

Views

Why if the Legendre symbol satisfy $\left(\frac{a}p\right)=\left(\frac{p}a\right)$ then $\left(\frac{a}p\right) = 1$?

Published on 25 Mar 2026 - 6:13

score 88 · Answer 7 · 2019-06-27 17:11:29

88

Views

How to find integer solutions of $x^2 + by = c$

Published on 27 Jun 2019 - 17:11

score 72 · Answer 8 · 2019-07-20 09:55:43

72

Views

Trying to use Eulers lemma for finding quadratic residues

Published on 20 Jul 2019 - 9:55

score 57 · Answer 9 · 2026-03-25 08:06:51

57

Views

Jacobi symbol:$(\frac{7m^2-1}{18m^2+1})=(\frac{25m^2}{18m^2+1})=1$?

Published on 25 Mar 2026 - 8:06

score 39 · Answer 10 · 2026-03-26 07:35:34

39

Views

Is it a good idea to check if prime candidate is of residue class $1$ modulo $4$ in Rabin-Miller Test?

Published on 26 Mar 2026 - 7:35

score 78 · Answer 11 · 2019-07-27 21:50:00

78

Views

Prove: If $4k+1$ is a Quadratic Nonresidue mod $p$ then $k$ is a Quadratic Residue mod $p$

Published on 27 Jul 2019 - 21:50

score 128 · Answer 12 · 2019-07-30 11:21:38

128

Views

Quadratic Residues in $\{a\}\cup\{ah^2+bh+c:0\leq h<p\}$

Published on 30 Jul 2019 - 11:21

score 204 · Answer 13 · 2019-08-02 10:59:55

204

Views

Are Quadratic Residues the way to the solutions of Quadratic Diophantine Equations?

Published on 02 Aug 2019 - 10:59

score 640 · Answer 14 · 2019-08-19 04:03:00

640

Views

Prove $r$ the smallest quadratic non-residue modulo $p \geq 3$ is prime

Published on 19 Aug 2019 - 4:03

score 277 · Answer 15 · 2026-03-25 09:28:13

277

Views

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

Published on 25 Mar 2026 - 9:28

List Question

$\forall p \ge 11 \quad \exists n \in \{1,2,\dots,9\}$ such that $n$ and $n+1$ are quadratic residues mod p

Solutions of $x^2 \equiv 1 \pmod N$

Show that a following equation has no solution in integers: $x^3-x+9=5y^2$

Let $p$ be a prime of the form $p = a^2 + b^2$ with $a,b \in \mathbb{Z}$ and $a$ an odd prime. Prove that $(a/p) =1$

Show that a is a quadratic residue modulo $p$ iff $ind_{r} (\mathbb{a})$ is even.

Why if the Legendre symbol satisfy $\left(\frac{a}p\right)=\left(\frac{p}a\right)$ then $\left(\frac{a}p\right) = 1$?

How to find integer solutions of $x^2 + by = c$

Trying to use Eulers lemma for finding quadratic residues

Jacobi symbol:$(\frac{7m^2-1}{18m^2+1})=(\frac{25m^2}{18m^2+1})=1$?

Is it a good idea to check if prime candidate is of residue class $1$ modulo $4$ in Rabin-Miller Test?

Prove: If $4k+1$ is a Quadratic Nonresidue mod $p$ then $k$ is a Quadratic Residue mod $p$

Quadratic Residues in $\{a\}\cup\{ah^2+bh+c:0\leq h<p\}$

Are Quadratic Residues the way to the solutions of Quadratic Diophantine Equations?

Prove $r$ the smallest quadratic non-residue modulo $p \geq 3$ is prime

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

Trending Questions

Popular # Hahtags

Popular Questions