Problem

Source: 2018 China Northern MO, Grade 11, Problem 4

Tags: absolute value, combinatorics



For $n(n\geq3)$ positive intengers $a_1,a_2,\cdots,a_n$. Put the numbers on a circle. In each operation, calculate difference between two adjacent numbers and take its absolute value. Put the $n$ numbers we get on another ciecle (do not change their order). Find all $n$, satisfying that no matter how $a_1,a_2,\cdots,a_n$ are given, all numbers on the circle are equal after limited operations.