Question 124
There are $n \geqslant 3$ positive integers written on a blackboard. A move consists of choosing three numbers $a, b, c$ on the blackboard such that they are the sides of a non-degenerate non-equilateral triangle and replacing them by $a+b-c$, $b+c-a$ and $c+a-b$.
Show that an infinite sequence of moves cannot exist.
Show that an infinite sequence of moves cannot exist.