Also found in: Acronyms, Wikipedia.

(mathematics)
A residue of order 2.

This relation was discovered about 1772 by L. Euler, a modern formulation was given by A. Legendre, and a complete proof was first given in 1801 by K. Gauss. A convenient generalization of the Legendre symbol is the Jacobi symbol. There are many generalizations of the law of quadratic reciprocity in the theory of algebraic numbers. The distribution of quadratic residues and of the sums of the values of the Legendre symbol has been studied by I. M. Vinogradov and other mathematicians.

### REFERENCE

Vinogradov, I. M. Osnovy teorii chisel Moscow, 1972.
References in periodicals archive ?
Let * = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the quadratic residue character, which is 1 on the quadratic residues Q [subset] GF[(p).
We call this a long quadratic residue code, or LQR code for short, and identify it with a subset of [F.
Voloch, Double circulant quadratic residue codes, IEEE Transactions in Information Theory, Volume 50, Issue 9, Sept.
Voloch, Asymptotics of the minimal distance of quadratic residue codes, preprint.
Q](GF(p))j = 1:5p + a, where Q is the set of quadratic residues and a is a small constant, -1/2 [less than or equal to] a [less than or equal to] 5/2.
p], the set of quadratic residues modulo p, and secondly use all these results to determine the above number.
By [4], we know that the number of pairs of consecutive quadratic residues modulo p is given by the formula
p] = p - 3/4 is the number of quadratic residues at each column and hence we obtain the following result.
As every column (and row) has the same number of quadratic residues (and non-residues), we can consider the column consisting of the entries x + 1 (taking y = 1 [member of] [Q.

Site: Follow: Share:
Open / Close