Quadratic residue

From Academic Kids

In mathematics, a number q is called a quadratic residue modulo p if there exists an integer x such that:

<math>{x^2}\equiv{q}\mbox{ (mod }p\mbox{)}.<math>

Otherwise, q is called a quadratic non-residue.

In effect, a quadratic residue modulo p is a number that has a square root in modular arithmetic when the modulus is p. The law of quadratic reciprocity says something about quadratic residues and primes.

Quadratic residues are used in the Legendre symbol. Quadratic reciprocity and the Gauss lemma both reason about quadratic residues.

External links

es:residuo cuadrtico ja:平方剰余 pl:Reszta kwadratowa sv:Kvadratisk rest zh:二次剩余

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