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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On sequences containing at most $ 3$ pairwise coprime integers


Author: S. L. G. Choi
Journal: Trans. Amer. Math. Soc. 183 (1973), 437-440
MSC: Primary 10L10
MathSciNet review: 0327710
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Abstract: It has been conjectured by Erdös that the largest number of natural numbers not exceeding n from which one cannot select $ k + 1$ pairwise coprime integers, where $ k \geq 1$ and $ n \geq {p_k}$, with $ {p_k}$ denoting the kth prime, is equal to the number of natural numbers not exceeding n which are multiples of at least one of the first k primes. It is known that the conjecture holds for k = 1 and 2. In this paper we establish the truth of the conjecture for k = 3.


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

  • [1] P. Erdős, Extremal problems in number theory, Proc. Sympos. Pure Math., Vol. VIII, Amer. Math. Soc., Providence, R.I., 1965, pp. 181–189. MR 0174539

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0327710-7
Keywords: Pairwise coprime integers, primes
Article copyright: © Copyright 1973 American Mathematical Society