On sequences containing at most $3$ pairwise coprime integers
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- by S. L. G. Choi
- Trans. Amer. Math. Soc. 183 (1973), 437-440
- DOI: https://doi.org/10.1090/S0002-9947-1973-0327710-7
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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
- 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
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 183 (1973), 437-440
- MSC: Primary 10L10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0327710-7
- MathSciNet review: 0327710