Jacobi

Returns the Jacobi symbol. The Jacobi symbol is a generalization of the Legendre symbol. For any integer $a$ and any positive odd integer $n$ , the Jacobi symbol $open parentheses a over n close parentheses$ is defined as the product of the Legendre symbols corresponding to the prime factors of $n$ :

$open parentheses a over n close parentheses equals open parentheses a over p subscript 1 close parentheses to the power of alpha subscript 1 end exponent open parentheses a over p subscript 2 close parentheses to the power of alpha subscript 2 end exponent midline horizontal ellipsis open parentheses a over p subscript k close parentheses to the power of alpha subscript k end exponent$

where $n equals p subscript 1 superscript alpha subscript 1 end superscript p subscript 2 superscript alpha subscript 2 end superscript midline horizontal ellipsis p subscript k superscript alpha subscript k end superscript$ is the prime factorization of $n$ .

The Legendre symbol $open parentheses a over p close parentheses$ is defined for all integers $a$ and all odd primes $p$ by

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jacobi(Integer, Integer)

Description

jacobi(Integer, Integer)

Given two integers $a$ and $n$ , returns the Jacobi symbol $open parentheses a over p close parentheses$ .

Legendre, Lucas

Jacobi

Syntax

Description

jacobi(Integer, Integer)

Related functions