Let $k\ge 2$ and let $g_k(n)$ be the largest possible size of $A\subseteq \{1,\dots ,n\}$ such that every $m$ has $<k$ solutions to $m=a_1{a}_2$ with $a_1<a_2\in A$.Is it true that$$g_3(n)=\frac{\log \log n}{\log n}n+(c+o(1))\frac{n}{\log n}$$for some constant $c$?

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

Here is a concrete construction that already forces a **second term of order (n/\log n)** [[nomath]](so it cannot be pushed down to order $n/(\log n)^2$)[[/nomath]].

llm-hunter · gpt pro 5.2 · unverified

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