Problem 9

Statement
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.

Solution
The code, in C.

#include <stdio.h>

int pythTrip(void)
{
  int a,b,c,k,m,n;
  for(n=1;n<100;n++){
    for(m=n;m<100;m++){
      for(k=1;k<100;k++){
	a = k*2*m*n;
	b = k*(m*m-n*n);
	c = k*(m*m+n*n);
	if(a+b+c==1000)
	  return a*b*c;
      }
    }
  }
}

int main(void)
{
  printf("%d\n",pythTrip());
  return 0;
}

Answer
31875000

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