Jacobi symbol : jacobi_symbol

### 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`