On a problem of Erdös
A generalized version of a problem of P. Erdös is solved in the paper. If \(1< a_1< \cdots <a_s\) are positive integers and \(\sum^s_{i=1} a_i^{-1}<n\) then this sum cannot split into \(n\) parts in such a manner that all partial sums are \(\leq 1\). If \(\sum^s_{i=1} a_i^{-1} <n (1-e^{1-n})\) then the mentioned decomposition is possible.
scientific article; zbMATH DE number 1011049