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On the integrality of the elementary symmetric functions of $1, 1/3, …, 1/(2n-1)$

In: Mathematica Slovaca, vol. 65, no. 5
Chunlin Wang - Shaofang Hong
Detaily:
Rok, strany: 2015, 957 - 962
Kľúčové slová:
elementary symmetric function, harmonic series
O článku:
Erd\H{o}s 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.
Ako citovať:
ISO 690:
Wang, C., Hong, S. 2015. On the integrality of the elementary symmetric functions of $1, 1/3, …, 1/(2n-1)$. In Mathematica Slovaca, vol. 65, no.5, pp. 957-962. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0064

APA:
Wang, C., Hong, S. (2015). On the integrality of the elementary symmetric functions of $1, 1/3, …, 1/(2n-1)$. Mathematica Slovaca, 65(5), 957-962. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0064
O vydaní:
Publikované: 1. 10. 2015