### 7.1.26 Jacobi symbol

The Jacobi symbol is a generalization of the Legendre symbol (a/n) when n is not prime. Let

n=p1α1⋯pkαk

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.

- jacobi_symbol takes two arguments: a and n, integers.
- jacobi_symbol(a,n) returns the Jacobi symbol (a/n).

#### Examples

jacobi_symbol(25,12)

1 |  |  |  |  |  |  |  |  |  |

jacobi_symbol(35,12)

−1 |  |  |  |  |  |  |  |  |  |

jacobi_symbol(33,12)

0 |  |  |  |  |  |  |  |  |  |