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We show that every set $A$ of natural numbers with positive upper density canbe shifted to contain the restricted sumset $\{b_1 + b_2 : b_1, b_2\in B \text{and } b_1 \neq b_2 \}$ for some infinite set $B \subset A$.

A proof of Erd\H{o}s's $B+B+t$ conjecture