（Problem 9）Special Pythagorean triplet

A Pythagorean triplet is a set of three natural numbers, a  b  c, for which,

a² + b² = c²

For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

#include<stdio.h>
#include<math.h>
#include<string.h>
#include<ctype.h>
#include<stdlib.h>
#include<stdbool.h>

void show()
{
    int a,b,c;
    for(a=1; a<333; a++)
    {
        for(c=333; c<500; c++)
        {
            b=1000-a-c;
            if(a*a+b*b==c*c)
            {
                printf("%d\n",a*b*c);
                return;
            }
        }
    }
}

int main()
{
    show();
    return 0;
}

Answer:

31875000