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...
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)