Jacobi symbol

Let n be an odd positive integer, with prime factorizationMathworldPlanetmath p1e1pkek. Let a0 be an integer. The Jacobi symbol (an) is defined to be


where (api) is the Legendre symbol of a and pi.

A further generalization of the Legendre symbol, due to Kronecker, is the Kronecker symbolMathworldPlanetmath.

Title Jacobi symbol
Canonical name JacobiSymbol
Date of creation 2013-03-22 12:36:26
Last modified on 2013-03-22 12:36:26
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 9
Author mathwizard (128)
Entry type Definition
Classification msc 11A07
Classification msc 11A15
Related topic LegendreSymbol
Related topic KroneckerSymbol