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quadratic residue (Definition)

Let $ a,n$ be relatively prime integers. If there exists an integer $ x$ that satisfies

$\displaystyle x^2 \equiv a \pmod{n}$
then $ a$ is said to be a quadratic residue of $ n$. Otherwise, $ a$ is called a quadratic nonresidue of $ n$.



"quadratic residue" is owned by mathcam. [ full author list (2) | owner history (1) ]
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See Also: Legendre symbol, Euler's criterion

Also defines:  quadratic non-residue, quadratic nonresidue

Attachments:
cases when minus one is a quadratic residue (Theorem) by alozano
any nonzero integer is quadratic residue (Theorem) by pahio
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Cross-references: integers, relatively prime
There are 21 references to this entry.

This is version 4 of quadratic residue, born on 2001-10-28, modified 2008-01-25.
Object id is 622, canonical name is QuadraticResidue.
Accessed 8197 times total.

Classification:
AMS MSC: 11A15 (Number theory :: Elementary number theory :: Power residues, reciprocity)
Pending Errata and Addenda
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