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Title of Journal: Acta Math Hung

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Abbravation: Acta Mathematica Hungarica

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Springer Netherlands

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DOI

10.1016/j.apsusc.2003.08.073

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1588-2632

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On a problem in additive number theory

Authors: YongGao Chen JinHui Fang
Publish Date: 2011/09/14
Volume: 134, Issue: 4, Pages: 416-430
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Abstract

For a set A let PA be the set of all finite subset sums of A We prove that if a sequence B=b 1b 2⋯ of integers satisfies b 1≧11 and b n+1≧3b n +5 n=12… then there exists a sequence of positive integers A=a 1a 2⋯ for which PA=ℕ∖B On the other hand if a sequence B=b 1b 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 PA=ℕ∖B

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Other Papers In This Journal:
  1. Weightable quasi-uniformities
  2. Rings of quotients of some infinite dimensional path algebras
  3. The Baum–Katz theorem for dependent sequences
  4. On complete convergence in mean for double sums of independent random elements in Banach spaces
  5. A note on the generalized rank reduction
  6. Existence and optimality of w -non-adjacent forms with an algebraic integer base
  7. Veldsman’s classes of associative rings
  8. Atomic decompositions of martingale hardy–morrey spaces
  9. A characterization of polyharmonic functions
  10. A note on invariant sets of iterated function systems
  11. On complete convergence and the strong law of large numbers for pairwise independent random variables
  12. Polynomial approximation with an exponential weight on the real semiaxis
  13. Best L 1 Approximation of Truncated Functions, Whitney-Type and Borh–Favard-Type Inequalities
  14. On the latticity of projection and antiprojection sets in Orlicz-Musielak spaces
  15. A categorical approach to absolute closure
  16. Planar zero divisor graphs of partially ordered sets
  17. On powers of relational and algebraic systems
  18. Inequalities for entire functions of exponential type satisfying $$ f(z) \equiv e^{i\gamma } e^{i\tau z} \overline {f(\bar z)} $$
  19. Local stability of a generalized Cauchy equation in Banach spaces
  20. A note on W - I -continuous functions
  21. A Remark on The Geometry of Spaces of Functions with Prime Frequencies
  22. Hua’s theorem with nine almost equal prime variables
  23. A weak type inequality for the maximal operator of ( C, α )-means of Fourier series with respect to the Walsh-Kaczmarz system
  24. Unification of generalized open sets on topological spaces
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