quadratic residue QuadraticResidue 2001-10-28 17:24:39 2008-01-25 17:54:29 Definition quadratic non-residue quadratic nonresidue \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $a,n$ be relatively prime integers. If there exists an integer $x$ that satisfies $$x^2 \equiv a \pmod{n}$$ then $a$ is said to be a \emph{quadratic residue} of $n$. Otherwise, $a$ is called a \emph{quadratic nonresidue} of $n$.