The Jacobi function returns three values: 0, if both a and n have a 
divisor in common which is greater than 1; -1 if a is a QNR of n; 
and +1 if a is a QR of n. 

Jacobi(a,n) 
{
  j := 1;
    while (a not 0) do 
    {
      while (a even) do 
      {
      a := a/2;
      if (n = 3 (mod 8) or n = 5 (mod 8)) then j := -j;
      }
    b := n; n := a; a := b;
    if (a = 3 (mod 4) and n = 3 (mod 4)) then j := -j;
    a := a mod n;
    }
  if (n = 1) then return (j) else return(0)
}

Example 2: Jacobi algorithm.