Erdős Distance Problem in $\mathbb{R}^d$

In this paper, we prove Erdős distance conjecture in $\mathbb{R}^d$, namely, a set of $n$ points in $\mathbb{R}^2$ determines $Ω(\frac{n}{\sqrt{\log n}})$ distances, and for $d\ge 3$, a set of $n$ points in $\mathbb{R}^d$ determines $Ω(n^{\frac{2}{d}})$ distinct distances.

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