Problem 89

Erdős Problem #89: declared status 'open'. Formalized: yes. Does every set of $n$ distinct points in $\mathbb{R}^2$ determine $\gg n/\sqrt{\log n}$ many distinct distances? Current best: A $\sqrt{n}\times\sqrt{n}$ integer grid shows that this would be the best possible. Prize: $500. OEIS: A131628, A186704. Tags: distances, geometry.