Kronecker Symbol

The Kronecker symbol extends the Jacobi symbol, itself a generalization of the Legendre symbol, to all integers as its lower argument, including negative numbers, even numbers and zero. It preserves the multiplicative properties that make the Legendre and Jacobi symbols useful for determining quadratic residues, while removing the restriction that the lower argument be an odd positive integer. Named after Leopold Kronecker, the symbol is used in class field theory and in efficient algorithms for testing quadratic residuosity, and it appears in the definition of certain L-functions in algebraic number theory. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/