Quadratic nonresidue

Definition

Suppose $\text{[math]}$ is a natural number. A quadratic nonresidue modulo $\text{[math]}$ is a number $\text{[math]}$ (or a residue class of a number $\text{[math]}$ ) relatively prime to $\text{[math]}$ such that the equation:

$\text{[math]}$

has no solution. Since $\text{[math]}$ is relatively prime to $\text{[math]}$ , it suffices to check that there is no solution with $\text{[math]}$ relatively prime to $\text{[math]}$ . Further, it suffices to check that there is no solution for $\text{[math]}$ relatively prime to $\text{[math]}$ and $\text{[math]}$ .

Note that the term quadratic nonresidue is used both for actual numbers and for residue classes. The term is not used in cases where $\text{[math]}$ is not relatively prime to $\text{[math]}$ .

The opposite of quadratic nonresidue is quadratic residue.

Quadratic nonresidue

Definition

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