Let $n > 0$ be an odd and positive integer with the factorization $n=p_1^{e_1}\cdots p_r^{e_r}.$ For an integer $a\in\mathbb Z,$ the Jacobi symbol of $a$ modulo $n$ is an arithmetic function defined by
$$\left(\frac an\right):=\left(\frac a{p_1}\right)^{e_1}\cdots \left(\frac a{p_r}\right)^{e_r},$$ where $\left(\frac a{p_i}\right)$ denote the Legendre symbols of $a$ modulo the prime numbers $p_i$ dividing $n.$
Algorithms: 1
Explanations: 2
Proofs: 3
Theorems: 4
