ON THE INTEGRALITY OF THE ELEMENTARY SYMMETRIC FUNCTIONS OF 1, 1/3, ..., 1/(2n-1)

被引：7
|
作者：
Wang, Chunlin [1 ]
Hong, Shaofang [1 ]
机构：
[1] Sichuan Univ, Math Coll, Chengdu 610064, Peoples R China
来源：
MATHEMATICA SLOVACA | 2015年 / 65卷 / 05期
基金：
美国国家科学基金会;
关键词：
elementary symmetric function; harmonic series;
D O I：
10.1515/ms-2015-0064
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Erdos and Niven proved that for any positive integers m and d, there are only finitely many positive integers n for which one or more of the elementary symmetric functions of 1/m, 1/(m + d),...,1/(m + nd) are integers. In this paper, we show that if n >= 2, then none of the elementary symmetric functions of 1, 1/3,..., 1/(2n - 1) is an integer. (C) 2015 Mathematical Institute Slovak Academy of Sciences
引用
收藏
页码：957 / 962
页数：6
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