Definition:Jacobi Symbol

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 $$n = \prod_{i=1}^r p_i^{k_i}$$.

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

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