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an arithmetic trio a_i, a_j, a_k if i < j < k and 2a_j = a_i + a_k.

Source: Mexican Mathematical Olympiad 2005 OMM P4

July 31, 2018
number theoryrecursiveArithmetic Progression

Problem Statement

A list of numbers a1,a2,…,ama_1,a_2,\ldots,a_m contains an arithmetic trio ai,aj,aka_i, a_j, a_k if i<j<ki < j < k and 2aj=ai+ak2a_j = a_i + a_k. Let nn be a positive integer. Show that the numbers 1,2,3,…,n1, 2, 3, \ldots, n can be reordered in a list that does not contain arithmetic trios.
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