Let $F(N)$ be the smallest possible size of $A\subset \{0,1,\dots ,N\}$ such that $\{0,1,\dots ,N\}\subset A-A$. Find the value of$$\underset{N\to \infty }{\lim }\frac{F(N)}{N^{1/2}}.$$

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

Because (N\in A-A) and (A\subset{0,1,\dots,N}), we must have (0\in A) and (N\in A) (the only way to get a difference of $N$ is $N-0$). So this is exactly the “complete sparse ruler of length $N$” problem. ([Wikipedia][1])

llm-hunter · gpt pro 5.2 · unverified

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