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Give me a bound of $g(k)$

Source: Tuymaada 2020 Senior, Problem 4

October 6, 2020
combinatoricsfreedistance

Problem Statement

For each positive integer kk, let g(k)g(k) be the maximum possible number of points in the plane such that pairwise distances between these points have only kk different values. Prove that there exists kk such that g(k)>2k+2020g(k) > 2k + 2020.
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