Xiaowei Jiang

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math.NT2018

A certain reciprocal power sum is never an integer

Junyong Zhao, Shaofang Hong, Xiao Jiang

By $(Z^{+})^{\infty}$ we denote the set of all the infinite sequences $S = {s_{i}}_{i = 1}^{\infty}$ of positive integers (note that all the $s_{i}$ are not necessarily…

math.NT2018

A generalization of a theorem of Nagell

Yulu Feng, Shaofang Hong, Xiao Jiang +1

Let $n$ be a positive integer. In 1915, Theisinger proved that if $n \geq 2$ , then the $n$ -th harmonic sum $\sum_{k = 1}^{n} \frac{1}{k}$ is not an integer. Let $a$ and $b$ be positive in…