Question 15
Is it possible to write $1400$ natural numbers (not necessarily distinct) around a circle such that $2021$ is used at least once and each number is the sum of the greatest common divisor of the two previous numbers and the greatest common divisor of the two next numbers? For example, if $a, b, c, d, e$ are five consecutive numbers on the circle then $c = \gcd(a, b) + \gcd(d, e)$.