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arXiv · 1109.1442

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

Yong-Gao Chen·Min Tang
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Abstract

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.

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Yong-Gao Chen, Min Tang. 2011-09-07. On the elementary symmetric functions of $1, 1/2, \ldots , 1/n$. https://doi.org/10.4169/amer.math.monthly.119.09.862

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