Problem

Source: 2013 China TST Quiz 2 Day 2 P2

Tags: arithmetic sequence, number theory, China TST, algebra proposed



Find the greatest positive integer $m$ with the following property: For every permutation $a_1, a_2, \cdots, a_n,\cdots$ of the set of positive integers, there exists positive integers $i_1<i_2<\cdots <i_m$ such that $a_{i_1}, a_{i_2}, \cdots, a_{i_m}$ is an arithmetic progression with an odd common difference.