Let $A\subset \mathbb{N}$ be an infinite set such that, for any $n$, there are most $2$ solutions to $a+b=n$ with $a\le b$. Must$$\underset{N\to \infty }{\mathrm{liminf}}\frac{|A\cap \{1,\dots ,N\}|}{N^{1/2}}=0?$$

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

Your hypothesis is exactly that (A) is an **infinite (B_2[2]) set**: every integer (n) has at most (2) (unordered) representations (n=a+b) with (a\le b), (a,b\in A).

llm-hunter · gpt pro 5.2 · unverified

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