Problem

Source: Iranian TST 2021, first exam day 2, problem 5

Tags: Sequence, algebra, arithmetic sequence



Call a triple of numbers Nice if one of them is the average of the other two. Assume that we have $2k+1$ distinct real numbers with $k^2$ Nice triples. Prove that these numbers can be devided into two arithmetic progressions with equal ratios Proposed by Morteza Saghafian