Newbetuts

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

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

Solving the Diophantine Equation $ax^2 + bx + c = dy^2 + ey + f$?

If $a$ is a quadratic residue modulo every prime $p$, it is a square - without using quadratic reciprocity.

Find all odd primes $p$ for which $15$ is a quadratic residue modulo $p$

elementary proof that infinite primes quadratic residue modulo $p$

Visualizing quadratic residues and their structure

Prove that if $p$ is an odd prime that divides a number of the form $n^4 + 1$ then $p \equiv 1 \pmod{8}$

Looking for a simpler solution about quadratic congruence [duplicate]

Quadratic residue

How to find the amount of solutions of polynomial congruence?

Is every non-square integer a primitive root modulo some odd prime?

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

Legendre symbol, second supplementary law

New posts in quadratic-residues

Calculating $\sqrt{-1}$

How to find the solution of $x^2\equiv 25\pmod{32}$?

Is there any simple trick to solve the congruence $a^{24}\equiv6a+2\pmod{13}$?

Is it possible to a root of a Gaussian integer be a Hurwitz quaternion?

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

No canonical non-quadratic residue for primes $\equiv 1 \bmod 8$?

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

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

Solving the Diophantine Equation $ax^2 + bx + c = dy^2 + ey + f$?

If $a$ is a quadratic residue modulo every prime $p$, it is a square - without using quadratic reciprocity.

Find all odd primes $p$ for which $15$ is a quadratic residue modulo $p$

elementary proof that infinite primes quadratic residue modulo $p$

Visualizing quadratic residues and their structure

Prove that if $p$ is an odd prime that divides a number of the form $n^4 + 1$ then $p \equiv 1 \pmod{8}$

Looking for a simpler solution about quadratic congruence [duplicate]

Quadratic residue

How to find the amount of solutions of polynomial congruence?

Is every non-square integer a primitive root modulo some odd prime?

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

Legendre symbol, second supplementary law