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Definition of Quadratic Residue: Suppose that $n$ is a positive integer. A residue $\bar a$, mod $n$, is called a quadratic residue, if there exists a residue $\bar b$, such that: $$\bar b^2 = \bar a,$$ in the sense of arithmetic mod $n$.
For example, $\bar 2$ is a quadratic residue, mod $7$, since $\bar 3^2 = \bar 9 = \bar 2$, mod $7$.
This definition logically relies on the following definitions and statements: Def/Residue
The following statements and definitions logically rely on the material of this page: State/Eulers criterion, and State/Half of nonzero residues are quadratic residues
To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Theory of quadratic residues, Clust/Modular arithmetic