Question

Find the primes $p$ such that the equation: $x^{2} + 7x + 39 = 0 $ has a solution modulo $ p $.

score 115 · Answer 1 · 2026-04-15 20:23:14

115

Views

Find the primes $p$ such that the equation: $x^{2} + 7x + 39 = 0 $ has a solution modulo $ p $.

Published on 15 Apr 2026 - 20:23

score 571 · Answer 2 · 2026-04-17 05:26:49

571

Views

Prove that $\sum_{X=0}^{p-1} \left(\frac{X^{2}+A}{p}\right)=-1$

Published on 17 Apr 2026 - 5:26

score 154 · Answer 3 · 2026-05-10 22:02:48

154

Views

Legendre Symbol: Prove that if $(a,p)=1$ and $p$ is an odd prime, then $\sum^p_{n=1}\left(\frac{an+b}{p}\right)=0$.

Published on 10 May 2026 - 22:02

score 110 · Answer 4 · 2026-04-17 14:46:52

110

Views

Show that if $n\geq 5$ then $1!+2!+3!+\ldots+n!\equiv 3 \pmod{5}$

Published on 17 Apr 2026 - 14:46

score 79 · Answer 5 · 2026-05-10 22:02:42

79

Views

Show that $p$ is a divisor of numbers $m^2 + 1$, $n^2 + 2$, if and only if it is a divisor of some number of the form $k^4 + 1$.

Published on 10 May 2026 - 22:02

score 538 · Answer 6 · 2026-04-13 23:47:46

538

Views

Show that the following sum of legendre symbols is -1.

Published on 13 Apr 2026 - 23:47

score 344 · Answer 7 · 2026-05-10 20:41:21

344

Views

Show that $\left(\frac{2}{p}\right) = \large(-1)^{\frac{p^2-1}{8}\large}$

Published on 10 May 2026 - 20:41

score 122 · Answer 8 · 2026-04-14 08:13:12

122

Views

Legendre symbol multiplicativity

Published on 14 Apr 2026 - 8:13

score 158 · Answer 9 · 2026-04-17 07:05:44

158

Views

Trying to prove $p \equiv 3 \pmod 4 \iff \sum\limits_{x\in\mathbb{F}_p} \left(\frac{x^3-x}{p} \right)=0$

Published on 17 Apr 2026 - 7:05

score 76 · Answer 10 · 2026-04-18 06:46:15

76

Views

If prime $p$ divides $m^2+1$ and $n^2+2$, then there exists $k$ such that $p$ divides $k^4+1$.

Published on 18 Apr 2026 - 6:46

score 136 · Answer 11 · 2026-04-17 11:08:20

136

Views

Show that x is a quadratic (non-)residue (mod p) if p ≡ ... (mod y)

Published on 17 Apr 2026 - 11:08

score 271 · Answer 12 · 2026-04-13 03:34:03

271

Views

Legendre symbols as multiplicative homomorphisms in number fields

Published on 13 Apr 2026 - 3:34

score 306 · Answer 13 · 2026-04-13 18:56:05

306

Views

How to prove this sum of those legendre symbols is -1?

Published on 13 Apr 2026 - 18:56

score 160 · Answer 14 · 2026-04-17 08:17:16

160

Views

Show that $x^2+x+23\equiv 0\mod 173$ has a solution $\iff \left(\frac{28}{173}\right) = 1$

Published on 17 Apr 2026 - 8:17

score 87 · Answer 15 · 2026-04-15 13:57:44

87

Views

Understanding why $(\frac{a}{p}) \equiv a^{(p-1)/2} \pmod p$ when $p \mid a$

Published on 15 Apr 2026 - 13:57

List Question

Find the primes $p$ such that the equation: $x^{2} + 7x + 39 = 0 $ has a solution modulo $ p $.

Prove that $\sum_{X=0}^{p-1} \left(\frac{X^{2}+A}{p}\right)=-1$

Legendre Symbol: Prove that if $(a,p)=1$ and $p$ is an odd prime, then $\sum^p_{n=1}\left(\frac{an+b}{p}\right)=0$.

Show that if $n\geq 5$ then $1!+2!+3!+\ldots+n!\equiv 3 \pmod{5}$

Show that $p$ is a divisor of numbers $m^2 + 1$, $n^2 + 2$, if and only if it is a divisor of some number of the form $k^4 + 1$.

Show that the following sum of legendre symbols is -1.

Show that $\left(\frac{2}{p}\right) = \large(-1)^{\frac{p^2-1}{8}\large}$

Legendre symbol multiplicativity

Trying to prove $p \equiv 3 \pmod 4 \iff \sum\limits_{x\in\mathbb{F}_p} \left(\frac{x^3-x}{p} \right)=0$

If prime $p$ divides $m^2+1$ and $n^2+2$, then there exists $k$ such that $p$ divides $k^4+1$.

Show that x is a quadratic (non-)residue (mod p) if p ≡ ... (mod y)

Legendre symbols as multiplicative homomorphisms in number fields

How to prove this sum of those legendre symbols is -1?

Show that $x^2+x+23\equiv 0\mod 173$ has a solution $\iff \left(\frac{28}{173}\right) = 1$

Understanding why $(\frac{a}{p}) \equiv a^{(p-1)/2} \pmod p$ when $p \mid a$

Trending Questions

Popular # Hahtags

Popular Questions