IMO 2020 Shortlist N3

Let n be an integer with n ě 2. Does there exist a sequence pa1,...,anq of positive integers with not all terms being eq...

IMO 2020 Shortlist N3

Category: Number Theory

Problem

Let n be an integer with n ě 2. Does there exist a sequence pa1,...,anq of positive integers with not all terms being equal such that the arithmetic mean of every two terms is equal to the geometric mean of some (one or more) terms in this sequence? (Estonia)