Erdős problem 272

Let $N\geq 1$ . What is the largest $t$ such that there are $A_1,\ldots,A_t\subseteq \{1,\ldots,N\}$ with $A_i\cap A_j$ a non-empty arithmetic progression for all $i\neq j$ ?

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

272.lean

Retained formal statement3 of 4

Szabo showed that the maximal $t$ is equal to $\frac{N^2}{2} + O(N^{5/3}\log^3N).$

FormalConjectures/ErdosProblems/272.leanErdos272.erdos_272.variants.szabo1 lineExact file

1(fun N => ↑(Erdos272.maxArithInterCard N) - ↑N ^ 2 / 2) =O[Filter.atTop] fun N => ↑N ^ (5 / 3) * Real.log ↑N ^ 3

SolvedStatement only, no proof