no 1 to 2030, replace consecutive (a,b) with (a-b)^{2020}, last remains
Source: Greek National 2020 p3 (Archimedes)
February 23, 2020
combinatoricsnumber theory
Problem Statement
On the board there are written in a row, the integers from until (included that) in an increasing order.
We have the right of ''movement'' :
We choose any two numbers that are written in consecutive positions and we replace the pair by the number .
We repeat the movement , many times until only one number remains written on the board. Determine whether it would be possible, that number to be:
(i) (ii)