Abstract
Let $\mca = (A_1,\ldots, A_n)$ be a sequence of nonempty finite sets of positive real numbers, and let $\mcb = (B_1,\ldots, B_n)$ be a sequence of infinite discrete sets of positive real numbers. A \emph{weighted real Egyptian number with numerators $\mathcal{A}$ and denominators $\mathcal{B}$} is a real number $c$ that can be represented in the form \[ c = \sum_{i=1}^n \frac{a_i}{b_i} \] with $a_i \in A_i$ and $b_i \in B_i$ for $i \in \{1,\ldots, n\}$. In this paper, classical results of Sierpiński for Egyptian fractions are extended to the set of weighted real Egyptian numbers.
Citation
Melvyn B. Nathanson. "Weighted real Egyptian numbers." Funct. Approx. Comment. Math. 60 (2) 155 - 166, June 2019. https://doi.org/10.7169/facm/1702
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