2000 consecutive integers on the board
Source: 2022 Saudi Arabia JBMO TST 1.3
November 3, 2022
combinatoricsconsecutive
Problem Statement
consecutive integers (not necessarily positive) are written on the board. A student takes several turns. On each turn, he partitions the integers into pairs, and substitutes each pair by the difference arid the sum of that pair (note that the difference does not need to be positive as the student may choose to subtract the greater number from the smaller one; in addition, all the operations are carried simultaneously). Prove that the student will never again write consecutive integers on the board.