Erdős problem 503 · problems.science

What is the size of the largest $A \subseteq \mathbb{R}^n$ such that every three points from $A$ determine an isosceles triangle? That is, for any three points $x$ , $y$ , $z$ from $A$ , at least two of the distances $|x - y|$ , $|y - z|$ , $|x - z|$ are equal.

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

503.lean

Retained formal statement3 of 5

When $n = 2$ , the answer is 6 (due to Kelly [ErKe47] - an alternative proof is given by Kovács [Ko24c]).

[ErKe47] Erdős, Paul and Kelly, L. M., Elementary Problems and Solutions: Solutions: E735. Amer. Math. Monthly (1947), 227-229. [Ko24c] Z. Kovács, A note on Erdős's mysterious remark. arXiv:2412.05190 (2024).

FormalConjectures/ErdosProblems/503.leanErdos503.erdos_503.variants.R21 lineExact file

1IsGreatest {x | ∃ A, ∃ (_ : A.IsIsosceles), A.ncard = x} 6

SolvedStatement only, no proof

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