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

页码：957 / 962

页数：6