New posts in Quadratic Residues

Finding quadratic residues without Legendre symbols

Prove this equation has no integer solutions: $x^p_{1}+x^p_{2}+\cdots+x^p_{n}+1=(x_{1}+x_{2}+\cdots+x_{n})^2$

Is there always a positive integer $a$ such that both $a^2-4$ and $a^2+4$ are quadratic non-residues $\bmod p$?

If $p$ is prime, then $x^2 +5y^2 = p \iff p\equiv 1,9 $ mod $(20)$.

Find smallest prime $p$ such that all primes $q < 40$ are quadratic non-residues $\pmod p$

Is there a univariate rational polynomial which represents only squares in $\mathbb{R}$ and $\mathbb{Q}_2$, but not all other $\mathbb{Q}_p$?

Proof that square of an $\sqrt{2 - 4q}$ is not an integer

Elementary proof for: If x is a quadratic residue mod p, then it is a quadratic residue mod p^k

Can every element of a finite field be written as a sum of two non-squares?

Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.