Encyclopedia > Quadratic residue

Article Content

Quadratic residue

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.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!