Power Residue

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Power Residue


If the congruence xn = a (mod m) has a solution, then a is called a power residue of m of the nth order. Here, n is an integer greater than 1, and m is an integer. When n = 2, a is said to be a quadratic residue of m; when n = 3, a is a cubic residue of m; and when n = 4, a is a biquadratic residue of m.


Vinogradov, I. M. Osnovy teorii chisel, 8th ed. Moscow, 1972.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Abstract For any positive integer n, let [a.sub.m](n) denote the m-th power residue of n.
Keywords: m-th power residue of n; Chebyshev's function; Asymptotic formula.
We will also use the following elementary result concerning gth power residues. Below, we write [[nu].sub.p](g) for the p-adic valuation of the integer g.

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