关于1,1/4,…,1/(3n-2)的初等对称函数的整性(英文)

On the integrality of the elementary symmetric functions of 1,1/4,…,1/(3n-2)

在1946年,Erds和Niven证明只有有限多个正整数n,使得1,1/2,…,1/n的一个或多个初等对称函数是整数.在本文中,我们研究算术级数(1+3i)i∞=0.我们证明当n≥2时,1,1/4,…,1/(3n-2)的所有初等对称函数都不是整数.

In 1946, Erd6s and Niven proved that there are at most finitely many positive integers n for which one or more of the elementary symmetric functions of 1,1/2, ……, 1/n are integers. In this paper, we show that if n ≥ 2, then none of the elementary symmetric functions of 1, 1/4, ..., 1/（3n-2） is an integer.