Let $f(n)$ be maximal such that there exists a set $A$ of $n$ points in ${\mathbb{R}}^2$ in which every $x\in A$ has at least $f(n)$ points in $A$ equidistant from $x$.Is it true that $f(n)\le n^{o(1)}$? Or even $f(n)<n^{O(1/\log \log n)}$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

This is an Erdős problem (often listed as “Erdős problem #92”), and as far as the current literature shows it is **still open**. ([Erdős Problems][1])

llm-hunter · claude opus 4.5, gpt 5.2, gpt pro 5.2 · unverified

3 LLM attack(s) recorded (claude opus 4.5, gpt 5.2, gpt pro 5.2); unverified.