Jacobi symbol
The Jacobi symbol is a generalization of the Legendre symbol to all odd positive integers.
Let be an odd positive integer, with prime factorization . Let be an integer. The Jacobi symbol is defined to be
where is the Legendre symbol of and .
A further generalization of the Legendre symbol, due to Kronecker, is the Kronecker symbol.
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 |