On the Erdős-Straus non-averaging set problem
A set \(S\) of integers is said to be non-averaging if the arithmetic mean of two or more elements of \(S\) does not belong to \(S\). Let \(f(n)\) denote the cardinality of a largest non-averaging subset of \(\{0,1,\ldots,n\}\). The problem of Erdős-Straus is to give upper and lower bounds for \(f(n)\). This paper contains an improvement upon results of E. G. Straus and the author, showing that \(f(n)\gg n^{1/5}\) for all sufficiently large \(n\) and \(f(n)\gg n^{1/5}(\log \log n)^{2/5}\) for infinitely many \(n\).
scientific article; zbMATH DE number 3981282