Length and denominators of Egyptian fractions. II
Using the notations and definitions of part I (see Zbl 0637.10006), and define moreover \[ L(a,N)=\min \left\{k: a/N=\sum^{k}_{i=1}1/n_ i,\;n_ 1<n_ 2<\ldots<n_ k,\;n_ i\in\mathbb Z_ 0\right\}, \] and \[ L(N)=\max \{L(a,N): 1\leq a<N\}. \] In this second paper, the author develops an algorithm which yields \[ L(N)\leq \frac{2 \log N}{\log \log N}\left(1+\frac{2 \log \log \log N}{\log \log N}\right) \] and \[ D(N)\leq N(\log N)^{2+\varepsilon}, \] where \(\varepsilon\to 0\) as \(N\to \infty\).
scientific article; zbMATH DE number 4037910