Successive Differences and Accumulations of the Jacobi Symbol

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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 .

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