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- W2904117225 abstract "By $(mathbb{Z}^+)^{infty}$ we denote the set of all the infinite sequences $mathcal{S}={s_i}_{i=1}^{infty}$ of positive integers (note that all the $s_i$ are not necessarily distinct and not necessarily monotonic). Let $f(x)$ be a polynomial of nonnegative integer coefficients. Let $mathcal{S}_n:={s_1, ..., s_n}$ and $H_f(mathcal{S}_n):=sum_{k=1}^{n}frac{1}{f(k)^{s_{k}}}$. When $f(x)$ is linear, Feng, Hong, Jiang and Yin proved in [A generalization of a theorem of Nagell, Acta Math. Hungari, in press] that for any infinite sequence $mathcal{S}$ of positive integers, $H_f(mathcal{S}_n)$ is never an integer if $nge 2$. Now let deg$f(x)ge 2$. Clearly, $0 0$, there are positive integers $n_1$ and $n_2$ and infinite sequences $mathcal{S}^{(1)}$ and $mathcal{S}^{(2)}$ of positive integers such that $1-varepsilon<H_f(mathcal{S}^{(1)}_{n_1})<1$ and $1<H_f(mathcal{S}^{(2)}_{n_2})<1+varepsilon$." @default.
- W2904117225 created "2018-12-22" @default.
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- W2904117225 date "2018-12-20" @default.
- W2904117225 modified "2023-09-27" @default.
- W2904117225 title "A certain reciprocal power sum is never an integer" @default.
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