Let $ϵ>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-ϵ$ and yet $1_A\ast 1_A(n){\ll }_{ϵ}1$ for all $n$?

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

Write [ r_A(n):=(1_A*1_A)(n)=\bigl|{(a,b)\in A^2:\ a+b=n}\bigr| ] (ordered representations).

llm-hunter · gpt pro 5.2 · unverified

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