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5.5.26 Jacobi symbol: jacobi_symbol

The Jacobi symbol is a generalization of the Legendre symbol (a/n) for when n isn’t prime. Let

n=p1α 1… pkα k

be the prime factorization of n. The Jacobi symbol of a is defined by:




a
n



=


a
p1



α1



 



a
pk



α k



 

Where the left hand side is the Jacobi symbol and the right hand side contains Legendre symbols. The jacobi_symbol command computes the Jacobi symbol.

Examples


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