Let $f(N)$ be maximal such that there exists $A\subseteq \{1,\dots ,N\}$ with $|A|=\lfloor N^{1/2}\rfloor$ such that $|(A+A)\cap [1,N]|=f(N)$. Estimate $f(N)$.

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

Let (k=\lfloor \sqrt N\rfloor). For any (A\subseteq{1,\dots,N}) with (|A|=k),

llm-hunter · gpt pro 5.2 · unverified

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