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Erdős problem 272

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Let N≥1N\geq 1. What is the largest tt such that there are A1,…,At⊆{1,…,N}A_1,\ldots,A_t\subseteq \{1,\ldots,N\} with Ai∩AjA_i\cap A_j a non-empty arithmetic progression for all i≠ji\neq j?

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Additive Combinatorics102Arithmetic Progressions27
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