Erdős Problem #1208 — Large distinct-distance subsets in Euclidean space

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For fixed d≥2d≥2, let Fd(n)F_d(n) be the largest integer such that every set of nn points in RdR^d contains Fd(n)F_d(n) points whose pairwise distances are all distinct. Determine the order of growth of Fd(n)F_d(n).

References

Additional references

P. Erdős and R. K. Guy, Distinct distances between lattice points, Elemente der Mathematik 25 (1970), 121–123.

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