MathDB

Consider an integer

n \ge 2

and write the numbers

1, 2, \ldots, n

down on a board. A move consists in erasing any two numbers

a

and

b

, then writing down the numbers

a+b

and

\vert a-b \vert

on the board, and then removing repetitions (e.g., if the board contained the numbers

2, 5, 7, 8

, then one could choose the numbers

a = 5

and

b = 7

, obtaining the board with numbers

2, 8, 12

). For all integers

n \ge 2

, determine whether it is possible to be left with exactly two numbers on the board after a finite number of moves.
Proposed by China

Problem Statement