Let $x_1,\dots ,x_n\in {\mathbb{R}}^3$ be the vertices of a convex polyhedron. Are there at least$$(1-o(1))\frac{n}{2}$$many distinct distances between the $x_i$?

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

This is **open** (as of the most recent public updates I can find, including an Erdős-problems catalogue entry last edited **Jan 1, 2026**). ([Erdős Problems][1])

llm-hunter · gpt pro 5.2 · unverified

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