quadratic residue

Noun

 * 1)  For given positive integer n, any integer that is congruent to some square m2 modulo n.
 * 2) * 1991, John Stillwell (translator),, Lectures on Number Theory, [1863, Vorlesungen über Zahlentheorie], , , page 82,
 * If we now make the assumption that q is a quadratic residue of all odd primes z not greater than 2m + 1, then it follows from earlier theorems (§37) that the prime q, since it is $$\equiv$$ 1 (mod 8) and hence a quadratic residue of each power of 2, is also a quadratic residue of each number which has no odd prime factors except the prime numbers z
 * 1) * 1999, Dinakar Ramakrishnan, Robert J. Valenza, [清华大学出版社有限公司], Fourier Analysis on Number Fields, page 213,
 * Of special importance here is the quadratic reciprocity law, which for primes p and q gives a precise relationship between the status of p as a quadratic residue mod q and the status of q as a quadratic residue mod p.
 * Of special importance here is the quadratic reciprocity law, which for primes p and q gives a precise relationship between the status of p as a quadratic residue mod q and the status of q as a quadratic residue mod p.

Usage notes
An integer satisfying the criterion is said to be a quadratic residue modulo n. The trivial case m = 0 is usually excluded.

Translations

 * Danish: kvadratisk rest
 * Italian: residuo quadratico