Multiple reciprocal sums and multiple reciprocal star sums of polynomials are almost never integers

Shaofang Hong, Liping Yang, Qiuyu Yin +1

Let $n$ and $k$ be integers such that $1\le k\le n$ and $f(x)$ be a nonzero polynomial of integer coefficients such that $f(m)\ne 0$ for any positive integer $m$. For any $k$-tuple…