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On a problem of Nathanson

Volume 185 / 2018

Yong-Gao Chen, Min Tang Acta Arithmetica 185 (2018), 275-280 MSC: Primary 11B13; Secondary 11B75. DOI: 10.4064/aa171031-26-4 Published online: 29 June 2018


A set $A$ of nonnegative integers is an asymptotic basis of order $h$ if every sufficiently large integer can be represented as the sum of $h$ integers (not necessarily distinct) of $A$. An asymptotic basis $A$ of order $h$ is minimal if no proper subset of $A$ is an asymptotic basis of order $h$. We resolve a problem of Nathanson on minimal asymptotic bases of order $h$.


  • Yong-Gao ChenSchool of Mathematical Sciences
    and Institute of Mathematics
    Nanjing Normal University
    Nanjing 210023, P.R. China
  • Min TangSchool of Mathematics and Statistics
    Anhui Normal University
    Wuhu 241002, P.R. China

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