On a problem of Bleicher and Erdös

Hisashi Yokota

doi:10.1016/0022-314X(88)90017-0

On a problem of Bleicher and Erdös

Hisashi Yokota

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

3 Citations (Scopus)

Abstract

Let D(a, N) = min{n_k: a K = ∑₁^k 1 n₁, n₁ < n₂ < ⋯ < n_k, 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 language	English
Pages (from-to)	198-207
Number of pages	10
Journal	Journal of Number Theory
Volume	30
Issue number	2
DOIs	https://doi.org/10.1016/0022-314X(88)90017-0
Publication status	Published - 1988 Oct
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-314X(88)90017-0

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

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. Erd{\"o}s.",

author = "Hisashi Yokota",

year = "1988",

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AU - Yokota, Hisashi

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N2 - 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.

AB - 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.

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ER -

On a problem of Bleicher and Erdös

Abstract

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