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Erdos Discrepancy Problem Variation

Source: China Mathematical Olympiad 2015 Q6

December 21, 2014
combinatoricsalgebra

Problem Statement

Let a1,a2,...a_1,a_2,... be a sequence of non-negative integers such that for any m,nm,n ∑i=12main≤m. \sum_{i=1}^{2m} a_{in} \leq m. Show that there exist k,dk,d such that ∑i=12kaid=k−2014. \sum_{i=1}^{2k} a_{id} = k-2014.
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