sol2.c File Reference

Problem 9 solution More...

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

Include dependency graph for sol2.c:

Functions
int	main (void)
	Main function. More...

Detailed Description

Problem 9 solution

Author

Krishna Vedala

Problem Statement: A Pythagorean triplet is a set of three natural numbers, \(a < b < c\), for which, \(a^2 + b^2 = c^2\). For example, \(3^2 + 4^2 = 9 + 16 = 25 = 5^2\). There exists exactly one Pythagorean triplet for which \(a + b + c = 1000\). Find the product abc.

Given \(a^2 + b^2 = c^2\) and \(a+b+c = n\), we can write:

\begin{eqnarray*} b &=& \frac{n^2 - 2an}{2n - 2a}\\ c &=& n - a - b \end{eqnarray*}

Function Documentation

main()

int main

(

void

)

Main function.

{
    int N = 1000;
 
    for (int a = 1; a < 300; a++)
    {
        long tmp1 = N * N - 2 * a * N;
        long tmp2 = 2 * (N - a);
        div_t tmp3 = div(tmp1, tmp2);
        int b = tmp3.quot;
        int c = N - a - b;
 
        if (a * a + b * b == c * c)
        {
            printf("%d x %d x %d = %ld\n", a, b, c, (long int)a * b * c);
            return 0;
        }
    }
 
    return 0;
}