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equidistant points in R^3

Source: miklos schweitzer 1994 q7

October 16, 2021
equidistant pointscombinatorics

Problem Statement

Prove that there exist 0<α<β<10 < \alpha< \beta<1 numbers have the following properties. (i) for any sufficiently large n, n points can be specified in R3\Bbb R^3 , so that each point is equidistant from at least nαn^\alpha other points. (ii) the above statement is no longer true with nβn^\beta instead of nαn^\alpha
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