Let $k\ge 1$ and let $v(k)$ be the minimal integer which does not appear as some $n_i$ in a solution to$$1=\frac{1}{n_1}+\cdots +\frac{1}{n_k}$$with $1\le n_1<\cdots <n_k$. Estimate the growth of $v(k)$.

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

Write $D_k$ for the set of all integers $m$ that occur as *some* denominator $n_i$ in at least one $k$-term Egyptian fraction representation $ 1=\frac1{n_1}+\cdots+\frac1{n_k},\qquad 1<n_1<\cdots<n_k . $ [[nomath]](As you noticed, if $k\ge 2$ then $1$ can never occur among the $n_i$, so the standard definition is: **$v…

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

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