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An old question posed by Erdos asked whether there exists a set of n points such that c n distances occur more than n times. We provide an affirmative answer to this question, showing that there exists a set of n points such that n4 distances occur more than n times. We also present a generalized version, finding a set of n points where cₘ n distances occurring more than n+m times.
Krishnendu Bhowmick (Mon,) studied this question.