Definition:Jacobi Symbol

Definition
Let $m \in \Z$ be any integer and $n \in \Z$ be any odd integer such that $n \ge 3$.

Let the Prime Decomposition of $n$ be $\displaystyle n = \prod_{i=1}^r p_i^{k_i}$.

Then the Jacobi symbol $\displaystyle \left({\frac m n}\right)$ is defined as:
 * $\displaystyle \left({\frac m n}\right) = \prod_{i=1}^r \left({\frac m {p_i}}\right)^{k_i}$

where $\displaystyle \left({\frac m {p_i}}\right)$ is defined as the Legendre symbol.