perfect_squares_and_cubes_v1.c

/*

    perfect_squares_and_cubes_v1.c

    Task:
    a,b,c,d,e are five consecutive positive numbers such that
    (b+c+d) is a perfect square and
    (a+b+c+d+e) is a perfect cube.
    Find the smallest possible  values  of such  numbers.


    You can find all my C programs at Dragan Milicev's pastebin:

    https://pastebin.com/u/dmilicev

*/

#include <stdio.h>

// return square root of number if given number is perfect square, otherwise return 0.
int is_perfect_square(int number)
{
    int i;

    for(i=0; i<=number/4+1; i++)
        if(number == i*i)
            return i;

    return 0;
}

// return cube root of number if given number is perfect cube, otherwise return 0.
int is_perfect_cube(int number)
{
    int i;

    for(i=0; i<=number/8+1; i++)
        if(number == i*i*i)
            return i;

    return 0;
}


int main(void)
{
    int a, number_of_solutions=0, number_of_iterations=0;
/*
    a,  b,   c,   d,   e    are five consecutive positive numbers

    a, a+1, a+2, a+3, a+4

    b + c + d = a+1 + a+2 + a+3 = 3*a+6

    a + b + c + d = a + a+1 + a+2 + a+3 + a+4 = 5*a+10
*/

    for(a=1; a<700; a++)
    {
        number_of_iterations++;

        if( is_perfect_square(3*a+6) && is_perfect_cube(5*a+10) )
        {
            number_of_solutions++;
            printf("\n  a   b   c   d   e \n");
            printf(" %3d %3d %3d %3d% 3d \n", a, a+1, a+2, a+3, a+4 );
        }
    }

    if( number_of_solutions == 0 )
        printf("\n There is no such numbers. \n");
    else
        printf("\n\n There are %d such numbers. \n", number_of_solutions );

    printf("\n Number of iterations %d. \n", number_of_iterations );

    return 0;

} // main()