On a problem of Erdős and Graham

Hisashi Yokota

doi:10.1016/0022-314X(91)90052-D

On a problem of Erdős and Graham

Hisashi Yokota

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let m(l)=min {n₁ : 1 = Σ_i=1^l 1 n_i,n₁ < n₂ < ⋯ < n₁}, where the minimum ranges over all sets {n_i} of positive integers. Then there exists an increasing sequence of integers {l_k} such that m(l_k) l_k ≦ (log log l_k)³ which improves Erdo{combining double acute accent}s and Graham's result m(l_k) l_k ≦ (log l_k)².

Original language	English
Pages (from-to)	327-338
Number of pages	12
Journal	Journal of Number Theory
Volume	39
Issue number	3
DOIs	https://doi.org/10.1016/0022-314X(91)90052-D
Publication status	Published - 1991 Nov
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-314X(91)90052-D

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title = "On a problem of Erd{\H o}s and Graham",

abstract = "Let m(l)=min {n1 : 1 = Σi=1l 1 ni,n1 < n2 < ⋯ < n1}, where the minimum ranges over all sets {ni} of positive integers. Then there exists an increasing sequence of integers {lk} such that m(lk) lk ≦ (log log lk)3 which improves Erdo{combining double acute accent}s and Graham's result m(lk) lk ≦ (log lk)2.",

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AB - Let m(l)=min {n1 : 1 = Σi=1l 1 ni,n1 < n2 < ⋯ < n1}, where the minimum ranges over all sets {ni} of positive integers. Then there exists an increasing sequence of integers {lk} such that m(lk) lk ≦ (log log lk)3 which improves Erdo{combining double acute accent}s and Graham's result m(lk) lk ≦ (log lk)2.

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On a problem of Erdős and Graham

Abstract

ASJC Scopus subject areas

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