We present an explicit subset A⊆ N = \0,1,…\ such that A + A = N and for all ε > 0, \[limN→ ∞{|\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)∈ A^2\}|}{Nε} = 0.\] This answers a question of Erd{o}s.
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Jain et al. (2024) studied this question.
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