%0 Journal Article
%T On the elementary symmetric functions of $1, 1/2, \ldots , 1/n$
%A Yong-Gao Chen
%A Min Tang
%J Mathematics
%D 2011
%I arXiv
%R 10.4169/amer.math.monthly.119.09.862
%X In 1946, P. Erd\H os and I. Niven proved that there are only finitely many positive integers $n$ for which one or more elementary symmetric functions of $1, 1/2, \ldots , 1/n$ are integers. In this paper we solve this old problem by showing that if $n\ge 4$, then none of elementary symmetric functions of $1, 1/2, \ldots , 1/n$ is an integer.
%U http://arxiv.org/abs/1109.1442v1