Given $n$ points in ${\mathbb{R}}^2$ the number of distinct unit circles containing at least three points is $o(n^2)$.

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

This statement is **not proved** in general. It is a well-known **open problem of Erdős**.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.