On a conjecture of M. N. Bleicher and P. Erdös

Hisashi Yokota

doi:10.1016/0022-314X(86)90060-0

On a conjecture of M. N. Bleicher and P. Erdös

Hisashi Yokota

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

3 Citations (Scopus)

Abstract

Let D(a, N) = min{n_k: a N = Σ₁^k 1 n_i, n₁ < n₂ < ... < n_k, n_i ∈ Z}, where minimum ranges over all expansions of a N, and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(MN) ≤ max{MD(N), ND(M)} ≤ D(M) D(N), establishing a conjecture made by M. N. Bleicher and P. Erdös.

Original language	English
Pages (from-to)	89-94
Number of pages	6
Journal	Journal of Number Theory
Volume	24
Issue number	1
DOIs	https://doi.org/10.1016/0022-314X(86)90060-0
Publication status	Published - 1986 Sept
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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title = "On a conjecture of M. N. Bleicher and P. Erd{\"o}s",

abstract = "Let D(a, N) = min{nk: a N = Σ1k 1 ni, n1 < n2 < ... < nk, ni ∈ Z}, where minimum ranges over all expansions of a N, and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(MN) ≤ max{MD(N), ND(M)} ≤ D(M) D(N), establishing a conjecture made by M. N. Bleicher and P. Erd{\"o}s.",

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PY - 1986/9

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N2 - Let D(a, N) = min{nk: a N = Σ1k 1 ni, n1 < n2 < ... < nk, ni ∈ Z}, where minimum ranges over all expansions of a N, and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(MN) ≤ max{MD(N), ND(M)} ≤ D(M) D(N), establishing a conjecture made by M. N. Bleicher and P. Erdös.

AB - Let D(a, N) = min{nk: a N = Σ1k 1 ni, n1 < n2 < ... < nk, ni ∈ Z}, where minimum ranges over all expansions of a N, and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(MN) ≤ max{MD(N), ND(M)} ≤ D(M) D(N), establishing a conjecture made by M. N. Bleicher and P. Erdös.

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On a conjecture of M. N. Bleicher and P. Erdös

Abstract

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