Problem

Source: ELMO 2018 #2, 2018 ELMO SL N3

Tags: algebra, Integer sequence



Consider infinite sequences $a_1,a_2,\dots$ of positive integers satisfying $a_1=1$ and $$a_n \mid a_k+a_{k+1}+\dots+a_{k+n-1}$$for all positive integers $k$ and $n.$ For a given positive integer $m,$ find the maximum possible value of $a_{2m}.$ Proposed by Krit Boonsiriseth