nLab Jacobi symbol

Redirected from "Legendre symbol".
Note: quadratic reciprocity law and Jacobi symbol both redirect for "Legendre symbol".

Idea

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

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