Quadratic residue
From Exampleproblems
In mathematics, a number q is called a quadratic residue modulo p if there exists an integer x such that:
Otherwise, q is called a quadratic non-residue. Roughly half of the residue classes are of each type. More precisely, for p > 2, there are
- (p − 1)/2
of each kind. They occur in a rather random pattern; this has been exploited in applications to acoustics.
In effect, a quadratic residue modulo p is a number that has a square root in modular arithmetic when the modulus is p. This concept plays a large part in classical number theory.
For more about quadratic residues see
- Legendre symbol
- law of quadratic reciprocity
- Gauss's lemma
- Zolotarev's lemma
- Paley graph
- distribution of quadratic residues
External links
es:residuo cuadrático fr:Résidu quadratique ja:平方剰余 pl:Reszta kwadratowa fi:Neliöjäännös sv:Kvadratisk rest zh:二次剩余
