/* We need standard IO */
#include <stdio.h>
#include "isqrt.c"

/* factor a number by Anon's method.  Generating relation that   */
/* generated this was  N = 2*y*p - p*p  */
/* d wrt p = 2*y-2*p-1 = 2*(y-p) -1 */
/* d wrt y = 2p */
/* Since we know p is less than y, both are positive, so we have
 * to run one of the variables negative...  We'll pick p
 * (and we know p is at least as small as the square root, and
 * y is at least as large as it.)
 * d wrt -p = - 2*y + 2*p -1 = -2(y-p)-1 
 */

main () {
  long n, p, q, y, s, t;

  printf ("Factor a positive odd number by anon's method\n");
  printf ("N = \n"); scanf ("%ld", &n);
  printf ("Factoring %ld\n", n);
  if (n<1) { printf ("N must be greater than zero\n"); return 1;}
  if ((n%2) == 0) { printf ("N must not be even.\n"); return 2;}

  s = isqrt (n);
  p = s; y = 0; t = 2*y*p - p*p  - n;

  while (t!=0) if (t<0) { t +=  p+p          ; y++; }
               else     { t +=  p+p - y-y - 1; p--; }

  q = 2*y-p;
  printf ("%ld*%ld=%ld\n",p,q,n);
}