# On Sets of Distances of n Points

@article{Erds1946OnSO, title={On Sets of Distances of n Points}, author={Paul Erd{\"o}s}, journal={American Mathematical Monthly}, year={1946}, volume={53}, pages={248-250} }

1. The function f(n). Let [P. ] be the class of all planar subsets P. of n points and denote by f(n) the minimum number of different distances determined by its n points for P,, an element of { P. }. Clearly, f(3) = 1 (with the three points forming the vertices of an equilateral triangle) f(4) = 2, f(5) = 2. The following theorem establishes rough bounds for arbitrary n. Though I have sought to improve this result for many years, I have not been able to do so.

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