Problem 9

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 whicha + b + c = 1000.

Find the product abc.

C++:

#include 
     
      using namespace std;int main(){    int n, c;    // a + b + c = n    // a^2 + b^2 = c^2    // a < b < c    // a + b > c    // a < n / 3    // b <= (n - a) / 2    // c = n - a - b    while(cin >> n) {        for(int a=1, maxa=n/3; a
     

C++(Truth):

#include 
     
      using namespace std;int main(){    int s, c;    while(cin >> s) {        for(int a=3, maxa=(s-3)/3; a<=maxa; a++) {            for(int b=a+1, maxb=(s-1-a)/2; b<=maxb; b++) {                c = s - a - b;                if(a + b <= c)                    continue;                if(a * a + b * b == c * c)                    cout << a * b * c << endl;            }        }    }    return 0;}