MathDB

There are

n \ge 3

positive integers written on a board. A move consists of choosing three numbers

a, b, c

written from the board such that there exists a non-degenerate non-equilateral triangle with sides

a, b, c

and replacing those numbers with

a + b - c, b + c - a

and

c + a - b

.
Prove that a sequence of moves cannot be infinite.

Problem Statement