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- W2005666969 abstract "Erd{o}s and Niven proved in 1946 that for any positive integers $m$ and $d$, there are at most finitely many integers $n$ for which at least one of the elementary symmetric functions of $1/m, 1/(m+d), ..., 1/(m+(n-1)d)$ are integers. Recently, Wang and Hong refined this result by showing that if $ngeq 4$, then none of the elementary symmetric functions of $1/m, 1/(m+d), ..., 1/(m+(n-1)d)$ is an integer for any positive integers $m$ and $d$. Let $f$ be a polynomial of degree at least $2$ and of nonnegative integer coefficients. In this paper, we show that none of the elementary symmetric functions of $1/f(1), 1/f(2), ..., 1/f(n)$ is an integer except for $f(x)=x^{m}$ with $mgeq2$ being an integer and $n=1$." @default.
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- W2005666969 date "2014-02-13" @default.
- W2005666969 modified "2023-09-23" @default.
- W2005666969 title "The elementary symmetric functions of a reciprocal polynomial sequence" @default.
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- W2005666969 doi "https://doi.org/10.48550/arxiv.1402.3115" @default.
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