Let p be an odd prime, a be a positive number such that pa (i.e., p does not divide a), and let x be one of the numbers 1, 2, 3, ..., p-1. Then there is a unique x^', called the associate of x, such that

 xx^'=a (mod p)

with 0<x^'<p (Hardy and Wright 1979, p. 67). If x^'=x, then a is called a quadratic residue of p.

See also

Quadratic Residue

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Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, p. 67, 1979.

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Cite this as:

Weisstein, Eric W. "Associate." From MathWorld--A Wolfram Web Resource.

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