/*
 * Copyright 2002 Massachusetts Institute of Technology
 *
 * Permission to use, copy, modify, and distribute this software and
 * its documentation for any purpose and without fee is hereby
 * granted, provided that both the above copyright notice and this
 * permission notice appear in all copies, that both the above
 * copyright notice and this permission notice appear in all
 * supporting documentation, and that the name of M.I.T. not be used
 * in advertising or publicity pertaining to distribution of the
 * software without specific, written prior permission.  M.I.T. makes
 * no representations about the suitability of this software for any
 * purpose.  It is provided "as is" without express or implied
 * warranty.
 * 
 * THIS SOFTWARE IS PROVIDED BY M.I.T. ``AS IS''.  M.I.T. DISCLAIMS
 * ALL EXPRESS OR IMPLIED WARRANTIES WITH REGARD TO THIS SOFTWARE,
 * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT
 * SHALL M.I.T. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
 * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
 * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
 * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#include <err.h>
#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>

static void
make_repunit(mpz_t num, unsigned long rnum)
{

	/* Probably not the fastest way, but certainly the easiest. */
	mpz_set_ui(num, 10);
	mpz_pow_ui(num, num, rnum);
	mpz_sub_ui(num, num, 1);
	mpz_divexact_ui(num, num, 9);
}

int
main(int argc, char **argv)
{
	int pow;
	unsigned long rnum, rnum_div;
	char *ep;
	mpz_t num, den, rem, tmp;

	if (argc != 2)
		errx(1, "must supply R-number to factor as an argument");
	rnum = strtoul(argv[1], &ep, 10);
	if (*ep != '\0')
		errx(1, "could not parse argument");

	mpz_init(num);
	make_repunit(num, rnum);
	mpz_init(den);
	mpz_init(rem);
	mpz_init(tmp);

	for (rnum_div = 2; rnum_div < rnum; rnum_div++) {
		make_repunit(den, rnum_div);
		if (mpz_cmp(num, den) < 0)
			return 0;
		pow = 0;
		mpz_set(tmp, num);

		/* Inefficient but easy to follow. */
		mpz_mod(rem, num, den);
		while (mpz_cmp_ui(rem, 0) == 0) {
			pow++;
			mpz_divexact(tmp, tmp, den);
			mpz_mod(rem, tmp, den);
		}
		if (pow) {
			printf("R%lu", rnum_div);
			if (pow > 1)
				printf("**%d", pow);
			printf("\n");
		}
	}
	return 0;
}