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News/Exact values and exact upper bounds for families of integers with arithmetic progression intersections (Erd\H{o}s Problem #272)
arxiv
PublishedJuly 28, 2026 at 4:00 AM
—neutral

Exact values and exact upper bounds for families of integers with arithmetic progression intersections (Erd\H{o}s Problem #272)

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arXiv:2607.23004v1 Announce Type: cross Abstract: Let $t(N)$ be the largest $t$ for which there exist distinct sets $A_1,\dots,A_t \subseteq \{1,\dots,N\}$ such that $A_i \cap A_j$ is a nonempty arithmetic progression for all $i \neq j$ (Erdos Problem #272). Simonovits and Sos proved $t(N)=O(N^2)$ a

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