Question

I was writing some code to calculate Pythagorean triples, but then I got some values which were not solutions. Here is the code:

#include <iostream>
#include <math.h>

using namespace std;

int main()
{
int j, counter = 0;
double candidate, sqrnbr;
for (int i = 400; i <= 500; i++) //note that the range is only from 400-500 since I am still testing the code
{
    for (j = i; j <= 500; j++)
    {
        candidate = i*i+j*j;
        sqrnbr=sqrt(candidate);
        if (candidate/sqrnbr==sqrnbr)
        {
           cout << i << " and " << j << " and " << sqrnbr << endl;
           counter++;
        }
    }

}
cout << counter << endl;
system("pause");
return 0;
}

One of the outputs it gave was 408, 410 and 578.415. Does anyone know why this happens?

Answer 1

You calculate a double and never check whether it’s an integer value, so you get double values. You don’t get a lot more because the square root is generally not representable as a double, so

candidate/sqrnbr == sqrnbr

is false for many values of candidate.

To generate Pythagorean triplets, use only integer arithmetic. And there are better methods than brute force, there’s a classic formula, all Pythagorean triplets are of the form

d*(m^2 - n^2), d*2*m*n, d*(m^2 + n^2)

for some d, m, n.