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Arithmetic series with an odd common difference

Source: 2013 China TST Quiz 2 Day 2 P2

March 31, 2013
arithmetic sequencenumber theoryChina TSTalgebra proposed

Problem Statement

Find the greatest positive integer mm with the following property: For every permutation a1,a2,⋯ ,an,⋯a_1, a_2, \cdots, a_n,\cdots of the set of positive integers, there exists positive integers i1<i2<⋯<imi_1<i_2<\cdots <i_m such that ai1,ai2,⋯ ,aima_{i_1}, a_{i_2}, \cdots, a_{i_m} is an arithmetic progression with an odd common difference.
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