Let $A=\{1\leq a_1 < a_2 < \cdots\}$ and $B=\{1\leq b_1 < b_2 < \cdots\}$ be sets of integers with
$a_n/b_n\to 1$.
If $A+B$ contains all sufficiently large positive integers then is it true that
$\limsup 1_A\ast 1_B(n)=\infty$?
A conjecture of Erdős and Sárközy.
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