On a problem in additive number theory |
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| Authors: | Yong-Gao Chen Jin-Hui Fang |
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| Affiliation: | 1.School of Mathematical Sciences and Institute of Mathematics,Nanjing Normal University,Nanjing,P.R. China;2.Department of Mathematics,Nanjing University of Information Science & Technology,Nanjing,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={b 1<b 2<⋯} of integers satisfies b 1≧11 and b n+1≧3b n +5 (n=1,2,…), then there exists a sequence of positive integers A={a 1<a 2<⋯} for which P(A)=ℕ∖B. On the other hand, if a sequence B={b 1<b 2<⋯} of positive integers satisfies either b 1=10 or b 2=3b 1+4, then there is no sequence A of positive integers for which P(A)=ℕ∖B. |
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