Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter December 9, 2015

On the Integrality of the Elementary Symmetric Functions of 1, 1/3, . . . , 1/(2n − 1)

  • Chunlin Wang and Shaofang Hong EMAIL logo
From the journal Mathematica Slovaca


Erdős 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


[1] DUSART, P.: Estimates of some functions over primes without R. H., arXiv:1002.0442 (To appear).Search in Google Scholar

[2] ERDŐS, P.-NIVEN, I.: Some properties of partial sums of the harmonic series, Bull. Amer. Math. Soc. 52 (1946), 248-251.10.1090/S0002-9904-1946-08550-XSearch in Google Scholar

[3] SCHOENFELD, L.: Sharper bounds for the Chebyshev functions θ(x) and ψ(x), II, Math. Comp. 30 (1976), 337-360.Search in Google Scholar

Received: 2012-11-13
Accepted: 2013-1-30
Published Online: 2015-12-9
Published in Print: 2015-10-1

Mathematical Institute Slovak Academy of Sciences

Downloaded on 28.3.2023 from
Scroll Up Arrow