Exact values and exact upper bounds for families of integers with arithmetic progression intersections (Erdős Problem #272)

Zhanfu Yang

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 \…