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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.
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