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Find all $n$ such that after $n-1$ moves it is possible to obtain $0$.

Source: Caucasus MO 2023

July 16, 2023

Problem Statement

Numbers 1,2,…,n1, 2,\ldots, n are written on the board. By one move, we replace some two numbers a,b a, b with the number a2−ba^2-b{}. Find all nn{} such that after n−1n-1 moves it is possible to obtain 00.
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