# Near optimal bounds for the Erdős distinct distances problem in high dimensions

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DOI: 10.1007/s00493-008-2099-1

- Cite this article as:
- Solymosi, J. & Vu, V.H. Combinatorica (2008) 28: 113. doi:10.1007/s00493-008-2099-1

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## Abstract

We show that the number of distinct distances in a set of *n* points in ℝ^{d} is *Ω*(*n*^{2/d − 2 / d(d + 2)}), *d* ≥ 3. Erdős’ conjecture is *Ω*(*n*^{2/d}).

### Mathematics Subject Classification (2000)

52C10## Copyright information

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