English

On the elementary symmetric functions of $1, 1/2, \ldots , 1/n$

Number Theory 2014-09-16 v1

Abstract

In 1946, P. Erd\H os and I. Niven proved that there are only finitely many positive integers nn for which one or more elementary symmetric functions of 1,1/2,,1/n1, 1/2, \ldots , 1/n are integers. In this paper we solve this old problem by showing that if n4n\ge 4, then none of elementary symmetric functions of 1,1/2,,1/n1, 1/2, \ldots , 1/n is an integer.

Keywords

Cite

@article{arxiv.1109.1442,
  title  = {On the elementary symmetric functions of $1, 1/2, \ldots , 1/n$},
  author = {Yong-Gao Chen and Min Tang},
  journal= {arXiv preprint arXiv:1109.1442},
  year   = {2014}
}

Comments

7pages