Question 99
On the blackboard are written in a line the numbers from $1$ to $2030$ in increasing turn. We have the possibility of the “movement” $K$: We select two numbers $\alpha$, $\beta$ from the blackboard written in successive positions and we substitute the pair ($\alpha$, $\beta$) with the number $(\alpha - \beta)^{2020}$.
We perform the movement as many times as we need in order to have on the blackboard only one number. Examine, if this number can be:
(a) $2020^{2020}$,
(b) $2021^{2020}$.
We perform the movement as many times as we need in order to have on the blackboard only one number. Examine, if this number can be:
(a) $2020^{2020}$,
(b) $2021^{2020}$.