Problem

Source: Romanian "Stars of Mathematics" Junior 2019 P3

Tags: combinatorics proposed, combinatorics



On a board the numbers $(n-1, n, n+1)$ are written where $n$ is positive integer. On a move choose 2 numbers $a$ and $b$, delete them and write $2a-b$ and $2b-a$. After a succession of moves, on the board there are 2 zeros. Find all possible values for $n$. Proposed by Andrei Eckstein