关于作为 2h 阶渐近基的 Bh[1]-set

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-08-20 DOI:10.1016/j.jnt.2024.07.006

Sándor Z. Kiss , Csaba Sándor

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引用次数: 0

摘要

设 h,k≥2 为整数。如果每一个足够大的正整数都可以写成来自 A 的 k 项之和，那么正整数集合 A 称为 k 阶渐近基。在本文中，我们用概率方法证明了作为 2h 阶渐近基的 Bh[1] 集的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Bh[1]-sets which are asymptotic bases of order 2h

Let $h, k \geq 2$ be integers. A set A of positive integers is called asymptotic basis of order k if every large enough positive integer can be written as the sum of k terms from A. A set of positive integers A is said to be a $B_{h} [g]$ -set if every positive integer can be written as the sum of h terms from A at most g different ways. In this paper we prove the existence of $B_{h} [1]$ sets which are asymptotic bases of order 2h by using probabilistic methods.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.