Denominators of Egyptian fractions

Hisashi Yokota

doi:10.1016/0022-314X(88)90041-8

Denominators of Egyptian fractions

Hisashi Yokota

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

7 Citations (Scopus)

Abstract

Let D(a,N) = min{n_k: a N = Σ₁^k 1 n_i, n₁ < n₂ < ... < n_k, n_i ε{lunate} Z₀}, where the minimum ranges over all expansions of a N, and let D(N) = max{D(a,N): 1 ≤ a < N}. Then D(N) N ≤ (logN)^{3 2+ε{lunate}}, where ε{lunate} →0 as N → ∞, improving the result of M.N. Bleicher and P. Erdös.

Original language	English
Pages (from-to)	258-271
Number of pages	14
Journal	Journal of Number Theory
Volume	28
Issue number	3
DOIs	https://doi.org/10.1016/0022-314X(88)90041-8
Publication status	Published - 1988 Mar
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-314X(88)90041-8

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title = "Denominators of Egyptian fractions",

abstract = "Let D(a,N) = min{nk: a N = Σ1k 1 ni, n1 < n2 < ... < nk, ni ε{lunate} Z0}, where the minimum ranges over all expansions of a N, and let D(N) = max{D(a,N): 1 ≤ a < N}. Then D(N) N ≤ (logN) 3 2+ε{lunate}, where ε{lunate} →0 as N → ∞, improving the result of M.N. Bleicher and P. Erd{\"o}s.",

author = "Hisashi Yokota",

year = "1988",

month = mar,

doi = "10.1016/0022-314X(88)90041-8",

language = "English",

volume = "28",

pages = "258--271",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

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T1 - Denominators of Egyptian fractions

AU - Yokota, Hisashi

PY - 1988/3

Y1 - 1988/3

N2 - Let D(a,N) = min{nk: a N = Σ1k 1 ni, n1 < n2 < ... < nk, ni ε{lunate} Z0}, where the minimum ranges over all expansions of a N, and let D(N) = max{D(a,N): 1 ≤ a < N}. Then D(N) N ≤ (logN) 3 2+ε{lunate}, where ε{lunate} →0 as N → ∞, improving the result of M.N. Bleicher and P. Erdös.

AB - Let D(a,N) = min{nk: a N = Σ1k 1 ni, n1 < n2 < ... < nk, ni ε{lunate} Z0}, where the minimum ranges over all expansions of a N, and let D(N) = max{D(a,N): 1 ≤ a < N}. Then D(N) N ≤ (logN) 3 2+ε{lunate}, where ε{lunate} →0 as N → ∞, improving the result of M.N. Bleicher and P. Erdös.

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U2 - 10.1016/0022-314X(88)90041-8

DO - 10.1016/0022-314X(88)90041-8

M3 - Article

AN - SCOPUS:38249028061

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VL - 28

SP - 258

EP - 271

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 3

ER -

Denominators of Egyptian fractions

Abstract

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