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Cyclic permutation of 1400 numbers having certain property

Source: 2021 Iran second round mathematical Olympiad P6

May 16, 2021
number theorycombinatoricsgreatest common divisor

Problem Statement

Is it possible to arrange 1400 positive integer ( not necessarily distinct ) ,at least one of them being 2021 , around a circle such that any number on this circle equals to the sum of gcd of the two previous numbers and two next numbers? for example , if a,b,c,d,ea,b,c,d,e are five consecutive numbers on this circle , c=gcd⁡(a,b)+gcd⁡(d,e)c=\gcd(a,b)+\gcd(d,e)
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