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Operations on numbers

Source: IMOC 2023 C6

September 9, 2023
combinatorics

Problem Statement

Given integer n≥3n \geq 3. 1,2,…,n1, 2, \ldots, n were written on the blackboard. In each move, one could choose two numbers x,yx, y, erase them, and write down x+y,∣x−y∣x + y, |x-y| in the place of x,yx, y. Find all integers XX such that one could turn all numbers into XX within a finite number of moves.
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