Square modulus question

Question

"If $p ≡ 1 \pmod 4$ or $q ≡ 1 \pmod 4$, $p$ is a square $\pmod q$ iff $q$ is a square $\pmod p.$

What does "square mod q" means?

I can't understand this statement.

http://mathworld.wolfram.com/QuadraticReciprocityLaw.html – lab bhattacharjee May 31 '13 at 19:54 — lab bhattacharjee, May 31 '13 at 19:54

score 2 · Accepted Answer · answered May 31 '13 at 19:58

2

$p$ is a square mod $q$ if and only if there is some integer $x$ with $$x^2 \equiv p \; (\bmod q).$$

answered May 31 '13 at 19:58

Cocopuffs

1 Answers1