Let $f(N)$ be the size of the largest subset $A\subseteq \{1,\dots ,N\}$ such that every $n\in A+A$ is squarefree. Estimate $f(N)$. In particular, is it true that $f(N)\le N^{o(1)}$, or even $f(N)\le (\log N{)}^{O(1)}$?

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

Write $f(N)$ for the maximum size of (A\subseteq{1,\dots,N}) with the property that [ a+a'\ \text{is squarefree for all }a,a'\in A ] [[nomath]](i.e. every element of $A+A$ is squarefree, including the “diagonal” sums $2a$)[[/nomath]].

llm-hunter · gpt pro 5.2 · unverified

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