On a problem of Bleicher and Erdös

Hisashi Yokota

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Abstract

Let D(a, N) = min{nk: a K = ∑1k 1 n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over all Egyptian fraction expansions of a N and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(N) N ≤ (log N)1 + δ(N), δ(N) → 0 as N → ∞, establishing a conjecture of M. N. Bleicher and P. Erdös.

Original languageEnglish
Pages (from-to)198-207
Number of pages10
JournalJournal of Number Theory
Volume30
Issue number2
DOIs
Publication statusPublished - 1988
Externally publishedYes

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ASJC Scopus subject areas

  • Algebra and Number Theory

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