List questions from legendre-symbol | MathQa

Cryptography: Solve $x^2 \equiv 331 \pmod{385}$ using modular arithmetic

Published on 28 Dec 2024 - 14:16

Why does the Legendre symbol $(\frac {p}{3}) = 1 $ if $p \equiv 1 \pmod 3$ and $-1$ if $p \equiv 2 \pmod 3$?

Published on 30 Dec 2024 - 7:55

If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.

Published on 06 Jan 2025 - 23:41

Prove that a quadratic equation has no roots in a congruence class

Published on 29 Dec 2024 - 19:03

Prove that there are no solutions to $x^2 + x + 1 \equiv 0$ (mod $n$) in $\mathbb{Z}/_{n}\mathbb{Z}$

Published on 12 Jan 2025 - 9:03

Legendre symbol $(-3/p)$ where $p = 1 \mod 3$

Published on 11 Jan 2025 - 5:12

Jacobi's Symbol

Published on 12 Jan 2025 - 16:06

Infinite graph with Legendre symbol .

Published on 25 Dec 2024 - 12:12

Sum of Legendre symbols: $\sum _{n=1}^p \left(\frac{an+b}{p}\right)=0$

Published on 30 Dec 2024 - 15:57

Use that $ (\mathbb{Z}/p\mathbb{Z})^{*} $ is cyclic to give a direct proof that $ \left( \frac{-3}{p} \right) = 1 $ when $ p \equiv 1\ (\bmod\ 3) $.

Published on 18 Dec 2024 - 23:14