Problem 213

Erdős Problem #213: declared status 'open'. Formalized: yes. Let $n\geq 4$. Are there $n$ points in $\mathbb{R}^2$, no three on a line and no four on a circle, such that all pairwise distances are integers? Current best: The best construction to date, due to Kreisel and Kurz [KK08], has $n=7$. Ascher, Braune, and Turchet [ABT20] have shown that there is a uniform upper bound on the size of such a set, conditional on the Bombieri-Lang conjecture. Prize: no. Tags: distances, geometry.