We say that $A \subset N$ is an essential component if $d_{s} (A + B) > d_{s} (B)$ for every $B \subset N$ with $0 < d_{s} (B) < 1$ where $d_{s}$ is the Schnirelmann density.Is $B = {2^{m} 3^{n} : m, n \geq 0}$ an essential component?

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number theory · open · possible · 0 attempts

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