自然数的划分及其加权表示函数

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2023-10-27 DOI:10.1017/s0004972723001053

SHUANG-SHUANG LI, YU-QING SHAN, XIAO-HUI YAN

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引用次数: 0

摘要

摘要对于任意正整数$k_1,k_2$和任意集合$A\subseteq \mathbb {N}$，设$R_{k_1,k_2}(A, N)$是方程$ N =k_1a_1+k_2a_2$与$a_1,a_2\在A$中的解的个数。设g为一个固定整数。证明了如果$k_1$和$k_2$是两个整数，且$2\le k_1<k_2$和$(k_1,k_2)=1$，则不存在任何集$A\subseteq \mathbb {N}$使得$R_{k_1,k_2}(A, N)-R_{k_1,k_2}(\ math_1 <k_2$)=g$，如果$1=k_1<k_2$，则存在一个集A使得$R_{k_1,k_2}(A, N)-R_{k_1,k_2}(\ math_1 <k_2}(\mathbb {N}\ set- A, N)对所有正整数N =1$。

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PARTITIONS OF NATURAL NUMBERS AND THEIR WEIGHTED REPRESENTATION FUNCTIONS

Abstract For any positive integers $k_1,k_2$ and any set $A\subseteq \mathbb {N}$ , let $R_{k_1,k_2}(A,n)$ be the number of solutions of the equation $n=k_1a_1+k_2a_2$ with $a_1,a_2\in A$ . Let g be a fixed integer. We prove that if $k_1$ and $k_2$ are two integers with $2\le k_1

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society

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