List questions from quadratic-residues | MathQA

$\sum_{x=0}^{p-1}(\frac{ax^2+bx+c}{p})=-(\frac{a}{p})$, for $p\geq5$ an odd prime with $p \nmid b^2-4ac$, where $(\frac{a}{p})$ is the Legendre symbol

Published on 14 Aug 2016 - 3:27

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

Published on 25 Mar 2026 - 17:40

$xy$ is a quadratic residue mod $p$ iff $x$ is a quadratic residue mod $p$, where $y$ be a (nonzero) quadratic residue mod $p$

Published on 17 Aug 2016 - 21:56

Least prime quadratic residue

Published on 23 Aug 2016 - 5:55

Numbers $a$ for which every Sophie Germain safe Prime ($2p+1$) it is a quadratic residue $\pmod {2p+1}$ $>$ $a$

Published on 28 Aug 2016 - 21:12

How to find pairs of primes satisfying certain properties?

Published on 31 Aug 2016 - 10:10

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

Published on 08 Sep 2016 - 11:24

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 25 Mar 2026 - 12:49

Prove that there are an infinite number of natural numbers that cannot be written as the sum of three squares.

Published on 29 Sep 2016 - 8:46

$\sum_{i=1}^{[ a/2]} [\frac {ib}{a} ] + \sum_{i=1}^{[ b/2]} [\frac {ja}{b} ] = [a/2][b/2] + [(a,b)/2].$

Published on 25 Mar 2026 - 11:14

Use the Law of Quadratic Reciprocity and the Chinese Remainder Theorem to determine when $6$ is a quadratic residue modulo $p$.

Published on 25 Mar 2026 - 12:49

Product of three primes that is a square modulo 389

Published on 17 Oct 2016 - 3:58

Square root of a number modulo $p$ where $p\equiv3\bmod4$

Published on 19 Oct 2016 - 2:46

Assuming that $r$ is a primitive root of the odd prime $p$ prove that $ r^{(p-1)/2}\equiv -1 \pmod p $ holds

Published on 21 Oct 2016 - 7:51

Cubic residues for primes congruent to 2 mod 3

Published on 21 Oct 2016 - 18:03