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On a problem of Chen and Fang related to infinite additive complements

2020/12/17 by Kiss, Sándor Z., Sándor, Csaba
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2012.09675

Abstract

Two infinite sets A and B of nonnegative integers are called additive complements if their sumset contains every nonnegative integer. In 1964, Danzer constructed infinite additive complements A and B with A(x)B(x) = (1 + o(1))x as x → ∞, where A(x) and B(x) denote the counting function of the sets A and B, respectively. In this paper we solve a problem of Chen and Fang by extending the construction of Danzer.

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