Key points are not available for this paper at this time.
We show that every set A A of natural numbers with positive upper Banach density can be shifted to contain the restricted sumset b 1 + b 2: b 1, b 2 ∈ B and b 1 ≠ b 2 \b₁ + b₂: b₁, b₂ B { and b₁ b₂ \} for some infinite set B ⊂ A B A.
Kra et al. (Thu,) studied this question.