NL-NWO 2016 Problem 3

Find all possible triples $(a, b, c)$ of positive integers with the following properties: • $gcd(a, b) = gcd(a, c) = gcd(b, c) = 1$ , • $a$ is a divisor of $a + b + c$ , • $b$ is a divisor of $a + b + c$ , • $c$ is a divisor of $a + b + c$ .

(Here $gcd(x,y)$ is the greatest common divisor of $x$ and $y$ .)