Problem

Source: 2021 Iran second round mathematical Olympiad P6

Tags: number theory, combinatorics, greatest common divisor



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 $a,b,c,d,e$ are five consecutive numbers on this circle , $c=\gcd(a,b)+\gcd(d,e)$