Question 74
Given a fixed natural number $n \gt 1$, 2019 natural numbers are placed around the circle in such a way that the product of any two neighboring numbers is a perfect $n$-th power. Is it always the case that the product of any (not necessarily neighboring) two numbers is also a perfect $n$-th power?
(A. Nikolaev, B. Rublyov)
(A. Nikolaev, B. Rublyov)