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  • 1 School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210046, P.R. China
  • | 2 Department of Mathematics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R. China
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Abstract

For a set A, let P(A) be the set of all finite subset sums of A. We prove that if a sequence B={b1<b2<⋯} of integers satisfies b1≧11 and bn+1≧3bn+5 (n=1,2,…), then there exists a sequence of positive integers A={a1<a2<⋯} for which P(A)=ℕ∖B. On the other hand, if a sequence B={b1<b2<⋯} of positive integers satisfies either b1=10 or b2=3b1+4, then there is no sequence A of positive integers for which P(A)=ℕ∖B.

  • [1] Burr, S. A. 1970 Erdős, P. Rényi, A. Sós, V. T. (eds.) Combinatorial Theory and its Applications III Coll. Math. Soc. J. Bolyai 4 North-Holland Publ. Comp. Amsterdam–London 1155.

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  • [2] Hegyvári, N. 1996 On representation problems in the additive number theory Acta Math. Hungar. 72 3544 .

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Acta Mathematica Hungarica
Language English
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1950
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)