Question 67
Martin wrote the pair of integers $(1011,1012)$ on the board. Then, every minute, if the pair $(a, b)$ is written on the board, he erases it and replaces it, as he chooses, by one of the pairs $(b, a)$, $(b+1, a-1)$ or $(b-2, a+2)$, with the only constraint that he writes only pairs whose two numbers are nonnegative.
Which pairs of integers can Martin write on the board after a finite number of such operations?
Which pairs of integers can Martin write on the board after a finite number of such operations?