Let $x_{1}, \dots, x_{n} \in R^{2}$ determine the set of distances ${u_{1}, \dots, u_{t}}$ . Suppose $u_{i}$ appears as the distance between $f (u_{i})$ many pairs of points. Then for all $ϵ > 0$ $i \sum f (u_{i})^{2} ≪_{ϵ} n^{3 + ϵ} .$

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geometry · solved · prize $500 · possible · 0 attempts

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