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arXiv · 2412.05190

A note on Erd\H{o}s's mysterious remark

Zoltán Kovács
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Abstract

We give an alternative proof of the statement, by using elimination from algebraic geometry, that the only set $S\subset\mathbb{R}^2$, $\left|S\right|=6$ such that all subsets that form a triangle are isosceles triangles, is the regular pentagon with its center. Our proof can be extended to answer some related questions raised by Erd\H{o}s.

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Zoltán Kovács. 2024-12-06. A note on Erd\H{o}s's mysterious remark. https://arxiv.org/abs/2412.05190

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