The study demonstrates an explicit subset of natural numbers achieving an additive basis, highlighting Erdős' question.
We present an explicit subset A⊆ N = \0,1,… \ such that A + A = N and for all ε > 0 , {equation*}lim N→ ∞ { | \{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)∈ A^2 \} |}{Nε} = 0.{equation*} This answers a question of Erdős.
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Jain et al. (2025) studied this question.
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