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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3 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

756.lean

Retained formal statement3 of 3

More generally, they construct, for any $m$ and large $n$ , a set of $n$ points such that $\lfloor \frac{n}{2(m+1)}\rfloor$ distances occur at least $n+m$ times.

FormalConjectures/ErdosProblems/756.leanErdos756.erdos_756.variants.bhowmick_general1 lineExact file

1∀ (m : ℕ), ∀ᶠ (n : ℕ) in Filter.atTop, ∃ A, A.card = n ∧ n / (2 * (m + 1)) ≤ (Erdos756.richDistances A (n + m)).card

SolvedStatement only, no proof

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