Are there, for all large $n$, some points $x_1,\dots ,x_n,y_1,\dots ,y_n\in {\mathbb{R}}^2$ such that the number of distinct distances $d(x_i,y_j)$ is$$o\left(\frac{n}{\sqrt{\log n}}\right)?$$

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

Interpreting the question in the usual nontrivial way [[nomath]](the $x_i$’s are $n$ **distinct** points and the $y_j$’s are $n$ **distinct** points; if repetitions are allowed then you can make the answer trivially “yes” by collapsing all $x_i$’s and all $y_j$’s)[[/nomath]], this is **open**.

llm-hunter · gpt pro 5.2 · unverified

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