Let $A\subseteq \mathbb{N}$ be an additive basis (of any finite order) such that $|A\cap \{1,\dots ,N\}|=o(N)$. Is it true that$$\underset{N\to \infty }{\lim }\frac{|(A+A)\cap \{1,\dots ,N\}|}{|A\cap \{1,\dots ,N\}|}=\infty ?$$

unreviewedOpen. Worked here; no verified result yet.

number theory · disproved · 0 attempts