The Jacobi symbol is a generalization of the Legendre symbol (a/n) when n is not prime. Let
| n=p1α 1⋯ pkα k |
be the prime factorization of n. The Jacobi symbol of a is defined by:
| ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ | = | ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ |
| … | ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ |
|
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(25,12) |
|
| jacobi_symbol(35,12) |
|
| jacobi_symbol(33,12) |
|