There are positive integers written on a blackboard. A move consists of choosing three numbers , , on the blackboard such that they are the sides of a non-degenerate non-equilateral triangle and replacing them by , and .
Show that an infinite sequence of moves cannot exist.
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.
Izvor: Srednjoeuropska matematička olimpijada 2016, pojedinačno natjecanje, problem 2
Školjka 
positive integers written on a blackboard. A move consists of choosing three numbers 
, 
, 
on the blackboard such that they are the sides of a non-degenerate non-equilateral triangle and replacing them by 
, 
and 
.