13 gcd(a, b) = lcm(a, b); a + b = 2016

#include <iostream>

using namespace std;

/*
Problem statement
Given that a and b are 2 integers such tat 13 gcd(a,b) = lcm(a, b)
and a + b = 2016, what are the values of a and b?
*/

// copied from other flie, great
// euclidian algorithm
unsigned gcd(unsigned u, unsigned v)
{
    while (v != 0)
    {
        unsigned r = u % v;
        u = v;
        v = r;
    }
    return u;
}

// ab = (a, b)[a, b]
// [a, b] = ab / (a, b)
unsigned lcm(unsigned u, unsigned v)
{
    return (u / gcd(u, v)) * v;
}

int main()
{
    for (int a = 1; a <= 2015; a++)
    {
        int b = 2016 - a;
        if (13 * gcd(a, b) == lcm(a, b))
        {
            cout << a << " " << b << endl;
            break;
        }
    }
    return 0;
}