nLab Jacobi symbol

Idea

(…)

$$k \in 2\mathbb{N} + 1 ,\,\; a \in \mathbb{Z} \;\;\;\;\;\;\;\; \vdash \;\;\;\;\;\;\;\; (a \vert k) \,\in\, \{-1, 0, + 1\}$$

Properties

$$(a \vert k) \,=\, \left\{ \begin{array}{ccc} 0 &if& gcd(a,k) \neq 1 \\ \pm 1 &if& gcd(a,k) = 1 \end{array} \right.$$

References

See also:

• Wikipedia: Jacobi symbol