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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Two proofs in combinatorial number theory


Authors: Jaroslav Nešetřil and Vojtěch Rödl
Journal: Proc. Amer. Math. Soc. 93 (1985), 185-188
MSC: Primary 11P68; Secondary 05A17
MathSciNet review: 766553
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Abstract: The aim of this paper is to present a short combinatorial proof of a theorem of P. Erdős on multiplicative bases of integers. A solution of a problem of P. Erdős and D. J. Newman is also presented.


References [Enhancements On Off] (What's this?)

  • [1] P. Erdős, On the multiplicative representation of integers, Israel J. Math. 2 (1964), 251–261. MR 0181619 (31 #5847)
  • [2] P. Erdős, Some applications of Ramsey’s theorem to additive number theory, European J. Combin. 1 (1980), no. 1, 43–46. MR 576765 (82a:10067)
  • [3] J. Nešetřil and V. Rödl, Simple proof of the existence of restricted Ramsey graphs by means of partite construction, Combinatorica 2 (1981), 199-202.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0766553-0
PII: S 0002-9939(1985)0766553-0
Keywords: Multiplicative base, Ramsey theorem, $ {B^{(k)}}$-sequence
Article copyright: © Copyright 1985 American Mathematical Society