/*
 * ammprobgmp.c
 *
 * Calculation for a problem from the American Mathematical Monthly.
 * (C version using the GNU MP library.)
 *
 * Warren Weckesser, Dept. of Mathematics, Colgate University
 *
 *
 * Compile with:
 *    gcc ammprobgmp.c -o ammprobgmp -lgmp
 */

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

#define ONE ((unsigned long) 1)

int main(int argc, char **argv)
    {
    /* Declare the variables that we will use. */
    mpz_t n, nlast;
    mpz_t m, root, rem;
    mpz_t n1;

    /* Check that the user gave two arguments to the command. */
    if (argc != 3)
        {
        printf("use: %s first last\n",argv[0]);
        return(-1);
        }

    /* Initialize the variables. */
    mpz_init_set_str(n,argv[1],10);
    mpz_init_set_str(nlast,argv[2],10);
    mpz_init(m);
    mpz_init(root);
    mpz_init(rem);
    mpz_init(n1);

    while (mpz_cmp(n,nlast) <= 0) /* while n <= nlast ... */
        {
        mpz_add_ui(n1,n,ONE);     /* n1 = n+1                                 */
        mpz_mul(m,n,n);           /* m = n*n                                  */
        mpz_add_ui(m,m,ONE);      /* m = m + 1 = n^2+1                        */
        mpz_mul(m,m,n1);          /* m = m*n1 = (n^2+1)(n+1) = n^3+n^2+n^1+1  */
        mpz_sqrtrem(root,rem,m);  /* Find root & rem such that root^2+rem = m */
        if (mpz_sgn(rem) == 0)    /* if rem == 0 ... */
            {
            /* Print n, m and root */
            mpz_out_str(stdout,10,n);
            printf(" ");
            mpz_out_str(stdout,10,m);
            printf(" ");
            mpz_out_str(stdout,10,root);
            printf("\n");
            }
        mpz_add_ui(n,n,ONE);      /* n = n + 1  */
        }
    return(0);
    }