You choose three POSITIVE integers: x, y and z.

The quotients 1. (x*y)/(x+y)

2. (x*z)/(x+z)

3. (y*z)/(y+z)

shall also be integers.

So, one has to prove the integers x, y and z have a factor in common which is bigger than 1.

The problem is that I absolutely don't know how to prove this.