Question 6
You are given three positive integers. A move consists of replacing $m \leq n$ by $2m$, $n - m$. Show that you can always make a series of moves which results in one of the integers becoming zero. [For example, if you start with $4, 5, 10$, then you could get $8, 5, 6$, then $3, 10, 6$, then $6, 7, 6$, then $0, 7, 12$. ]