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Fantastic number theory

Source: Kyiv City MO 2024 Round 2, Problem 11.2

February 4, 2024
number theoryDivisibility

Problem Statement

Mykhailo wants to arrange all positive integers from 11 to 20242024 in a circle so that each number is used exactly once and for any three consecutive numbers a,b,ca, b, c the number a+ca + c is divisible by b+1b + 1. Can he do it?
Proposed by Fedir Yudin