Let $k\ge 2$. Is it true that, for any distinct integers $1<n_1<\cdots <n_k$ such that$$1=\frac{1}{n_1}+\cdots +\frac{1}{n_k}$$we must have $\max (n_{i+1}-n_i)\ge 3$?

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

It is listed as **Erdős Problem #287** (Erdős–Graham) and is currently marked **open** (“falsifiable”: it could be disproved by a single explicit counterexample). ([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.