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no of arithmetical sets in A_n is greater than 2004

Source: 2004 Romania District VIII p3

August 15, 2024
combinatorics

Problem Statement

It is said that a set of three different numbers is an arithmetical set if one of the three numbers is the average of the other two. Consider the set An={1,2,...,n}A_n = \{1, 2,..., n\}, where nn is a positive integer, n≥3n\ge 3. a) How many arithmetical sets are in A10A_{10}? b) Find the smallest nn, such that the number of arithmetical sets in AnA_n is greater than 20042004.
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