Question 48
There are some integers written on the blackboard. In each step two numbers $a$ and $b$ are chosen and replaced with the numbers $3a - b$ and $13a - 3b$. If there are numbers $1$, $2$, $3$, $4$, $\ldots$, $2011$, $2012$ on the blackboard at the beginning, is it possible to get numbers $2$, $4$, $6$, $8$, $\ldots$, $4022$, $4024$ on the blackboard after a finite number of steps?