### 2.6.27 Jacobi symbol : `jacobi_symbol`

If *n* is not prime, the Jacobi symbol of *a*,
denoted as (*a*/*n*), is defined
from the Legendre symbol and from the
decomposition of *n* into prime factors.
Let

*n*=*p*_{1}^{α 1}..*p*_{k}^{α k} |

where *p*_{j} is prime and α _{j} is an integer for *j*=1..*k*.
The Jacobi symbol of *a* is defined by :

⎛
⎜
⎜
⎝ | | ⎞
⎟
⎟
⎠ | = | ⎛
⎜
⎜
⎝ | | ⎞
⎟
⎟
⎠ | | ... | ⎛
⎜
⎜
⎝ | | ⎞
⎟
⎟
⎠ | | |

`jacobi_symbol` takes two arguments *a* and *n*, and it returns the Jacobi
symbol (*a*/*n*).

Input :

`jacobi_symbol(25,12)`

Output :

`1`

Input :

`jacobi_symbol(35,12)`

Output :

`-1`

Input :

`jacobi_symbol(33,12)`

Output :

`0`