What is "jacobi symbol"

n. (context number theory English) Mathematical function of two integers, written $left(\{a\; over\; b\}right)$, based on whether ''a'' is a square modulo the prime factors of ''b''.

The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837, it is of theoretical interest in modular arithmetic and other branches of number theory, but its main use is in computational number theory, especially primality testing and integer factorization; these in turn are important in cryptography.