Successive Differences and Accumulations of the Jacobi Symbol
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Render modular results of successive accumulations or differences for Jacobi symbols for the range -59 to 59. The Jacobi symbol extends the Legendre symbol, allowing a generalization of Gauss's celebrated quadratic reciprocity theorem.
Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA
A number is called a quadratic residue modulo if there is a positive integer such that . The Jacobi symbol is 0 for numbers and with a common factor, 1 if is a quadratic residue modulo , and -1 otherwise. The Jacobi symbol reduces to the Legendre symbol if is an odd prime .