### 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=p1α 1..pkα k

where pj is prime and α j is an integer for j=1..k. The Jacobi symbol of a is defined by :

⎛
⎜
⎜
⎝

a
n

⎞
⎟
⎟
⎠

=

⎛
⎜
⎜
⎝

a
p1

⎞
⎟
⎟
⎠

α 1

...

⎛
⎜
⎜
⎝

a
pk

⎞
⎟
⎟
⎠

α k

`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`