Partitions of natural numbers with the same weighted representation functions
Partitions of natural numbers with the same weighted representation functions
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DOI：
10.1016/j.jnt.2012.06.005
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发表时间：
2012-12
影响因子：
0.7
通讯作者：
Quan-Hui Yang;Yong-Gao Chen
中科院分区：
文献类型：
--
作者：
Quan-Hui Yang;Yong-Gao Chen
正文：对于任何给定的两个正整数k1和k2以及任何非负整数集合A，令[公式：见文本]表示方程n= k1 a1 + k2 a2的解的个数，其中a1，a2∈A。在本文中，我们确定了所有的正整数对k1，k2存在一个集合A <$N，使得[公式：见正文]对所有n <$n0。我们还提出了几个问题，为进一步研究。视频：有关本文的视频摘要，请单击此处或访问http://www.youtube.com/watch? v= EnezEs100Y。
TEXT: For any given two positive integers k1and k2, and any set A of nonnegative integers, let [Formula: see text] denote the number of solutions of the equation n=k1a1+k2a2with a1,a2∈A. In this paper, we determine all pairs k1,k2of positive integers for which there exists a set A⊆N such that [Formula: see text] for all n⩾n0. We also pose several problems for further research. VIDEO: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=EnezEsJl0OY.