A basis of Zₘ

Min Tang; Yong-Gao Chen

A basis of Zₘ

Min Tang ; Yong-Gao Chen

Colloquium Mathematicae, Tome 106 (2006), p. 99-103 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $σ_{A} (n) = | (a, a^{'}) \in A ² : a + a^{'} = n |$ , where n ∈ N and A is a subset of N. Erdős and Turán conjectured that for any basis A of order 2 of N, $σ_{A} (n)$ is unbounded. In 1990, Imre Z. Ruzsa constructed a basis A of order 2 of N for which $σ_{A} (n)$ is bounded in the square mean. In this paper, we show that there exists a positive integer m₀ such that, for any integer m ≥ m₀, we have a set A ⊂ Zₘ such that A + A = Zₘ and $σ_{A} (n ̅) \leq 768$ for all n̅ ∈ Zₘ.

Publié le : 2006-01-01

Zbl 1138.11003

EUDML-ID : urn:eudml:doc:286391

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     year = {2006},
     pages = {99-103},
     zbl = {1138.11003},
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Min Tang; Yong-Gao Chen. A basis of Zₘ. Colloquium Mathematicae, Tome 106 (2006) pp. 99-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-1-6/