List questions from quadratic-reciprocity | MathQa

Prove that $\sum^{P}_{k=1} \lfloor\frac {ka}{p}\rfloor = \frac{p^{2} - 1}{8} + \mu(a,p)$ mod$(2)$

Published on 21 Dec 2024 - 16:40

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 13 Jan 2025 - 2:22

Let $p> 7$, prove that $\left(\frac{2}{q}\right) = (-1)^{\frac{q^2-1}{8}}$ with $q$ an odd prime

Published on 22 Dec 2024 - 4:36

Irreducibility in a polynomial related to quadratic residues

Published on 31 Dec 2024 - 15:13

Quadratic congruence with linear term

Published on 21 Dec 2024 - 13:18

If $p>3$ and $x^2+3y^2=p$, prove $\left(\frac{-3}{p}\right)=1$ and $p\equiv 1\pmod{6}$.

Published on 25 Dec 2024 - 6:13

Quadratic Reciprocity and Congruences

Published on 21 Dec 2024 - 6:26

Fermat's little theorem and Euler's criterion

Published on 31 Dec 2024 - 14:58

Quadratic reciprocity: Tell if $c$ got quadratic square root mod $p$

Published on 31 Dec 2024 - 13:00

Are there infinitely many pairs of primes, $p$ and $q$, such that $q = 4p + 1$?

Published on 31 Dec 2024 - 14:11