For integers $1\le a<b$ let $N(a,b)$ denote the minimal $k$ such that there exist integers $1<n_1<\cdots <n_k$ with$$\frac{a}{b}=\frac{1}{n_1}+\cdots +\frac{1}{n_k}.$$Estimate $N(b)={\max }_{1\le a<b}N(a,b)$. Is it true that $N(b)\ll \log \log b$?

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

$ \frac ab=\frac1{n_1}+\cdots+\frac1{n_k}\qquad (1<n_1<\cdots<n_k) $

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

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