OPENNOTORIOUSgeometrycombinatorial geometry
Does every set of $n$ distinct points in $\mathbb{R}^2$ determine $\gg n/\sqrt{\log n}$ many distinct distances?
Notes: A sqrt(n) x sqrt(n) integer grid shows this would be optimal. Guth and Katz proved there are always >> n/log n distinct distances. The remaining log factor is the gap.
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