Is it true that, for all sufficiently large $k$, there exist finite intervals $I_1,\dots ,I_k\subset \mathbb{N}$, distinct, not overlapping or adjacent, with $|I_i|\ge 2$ for $1\le i\le k$ such that$$1=\sum _{i=1}^k\sum _{n\in I_i}\frac{1}{n}?$$

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

As of **January 2026**, this is **not known**. In fact, with the conditions exactly as you stated (the (I_i) are **distinct**, **pairwise disjoint**, and **not adjacent**, and each has (|I_i|\ge 2)), it is recorded as an **open Erdős–Graham problem** (Erdős Problem #289). ([Erdős Problems][1])

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

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