Quadratic residue

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

Related Topics:
Mathematics - Modulo - Integer

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:{x^2}equiv{q}mbox{ (mod }pmbox{)}.

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Otherwise, q is called a quadratic non-residue.

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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.

Related Topics:
Square root - Modular arithmetic - Law of quadratic reciprocity - Primes

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

Related Topics:
Legendre symbol - Quadratic reciprocity - Gauss lemma

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