DK-GEORGMOHR 2024 Problem 4

Three different numbers are written on a blackboard. Each of the numbers are either $0$ or a positive integer. In each move, Alma may choose two numbers $a$ and $b$ , where $a > b$ , and replace them by $a^2 -b^2$ and $3a-b$ . After a finite number of moves Alma achieves that there are three identical numbers on the blackboard. Which numbers may have been on the blackboard at the beginning?