On a conjecture of M. N. Bleicher and P. Erdős
Let \(D(a,N)=\min \{n_ K:\) \(a/N=\sum^{K}_{1}(1/n_ i)\), \(n_ 1<n_ 2<...<n_ K\), \(n_ i\in {\mathbb{Z}}\}\), where minimum ranges over all expansions of a/N, and let \(D(N)=\max \{D(a,N):\quad 1\leq a<N\}.\) The author proves that if \(M\leq N\), then \(D(M N)\leq M D(N),\) and it implies that \(D(M N)\leq \max \{M D(N),\quad N D(M)\}\leq D(M) D(N),\) establishing a conjecture by M. N. Bleicher and P. Erdős.
scientific article; zbMATH DE number 3946220