Erdős problem 756 · problems.science

Let $A\subset \mathbb{R}^2$ be a set of $n$ points. Can there be $\gg n$ many distinct distances each of which occurs for more than $n$ many pairs from $A$ ?

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FormalConjectures/ErdosProblems/

756.lean

Retained formal statement1 of 3

Let $A\subset \mathbb{R}^2$ be a set of $n$ points. Can there be $\gg n$ many distinct distances each of which occurs for more than $n$ many pairs from $A$ ?

The answer is yes: Bhowmick [Bh24] constructs a set of $n$ points in $\mathbb{R}^2$ such that $\lfloor\frac{n}{4}\rfloor$ distances occur at least $n+1$ times.

FormalConjectures/ErdosProblems/756.leanErdos756.erdos_7561 lineExact file

1True ↔ (fun n => ↑n) =O[Filter.atTop] fun n => ↑(Erdos756.maxRichDistances n)

SolvedStatement only, no proof

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