MathDB

3

Part of 2020 Greece National Olympiad

Problems(1)

no 1 to 2030, replace consecutive (a,b) with (a-b)^{2020}, last remains

Source: Greek National 2020 p3 (Archimedes)

2/23/2020
On the board there are written in a row, the integers from 11 until 20302030 (included that) in an increasing order. We have the right of ''movement'' KK: We choose any two numbers a,ba,b that are written in consecutive positions and we replace the pair (a,b)(a,b) by the number (aāˆ’b)2020(a-b)^{2020}. We repeat the movement KK, many times until only one number remains written on the board. Determine whether it would be possible, that number to be: (i) 202020202020^{2020} (ii)202120202021^{2020}
combinatoricsnumber theory