ex09lista05

/*
It finds the Pythagorean triples (a, b, c), with a^2 + b^2 = c^2, under the restriction a + b + c = 1000.
The solution uses the relation b = 1000*(a - 500)/(a - 1000), which comes from solving the system of equations:
{ a^2 + b^2 = c^2,
{ a + b + c = 1000.
Also, since a, b and c are positive integers, it is only needed to swipe the interval 1 < a < 499.
*/

#include <stdio.h>
#include <math.h>

int main(){
 int    a, b, c, n = 0;
 double  dc, pc;

 for(a = 1; a <= 499; a++){
    b = 1000*(a - 500)/(a - 1000);
    dc = sqrt(a*a + b*b);

    modf(dc, &pc);
    c = (int)pc;

    if(c == (1000 - a - b)){
        printf("\nPythagorean Triple (%d): a = %3d, b = %3d, c = %3d\n", ++n, a, b, c);
        printf("Verifying: a+b+c = %3d, a^2+b^2 = %3d, c^2 = %3d\n", (a + b + c), (a*a + b*b), c*c);
    }
 }
}