It is well known [e.g., \textit{G. H. Hardy, J. E. Littlewood}, and \textit{G. Pólya}, ``Inequalities'' (1934; Zbl 0010.10703, 2nd ed. 1952; Zbl 0047.05302, reprint of the 2nd ed. 1988; Zbl 0634.26008), Theorem 84] that the power means \(M_{p}\) (including the geometric mean for \(p=0\)) are the only positively homogeneous quasiarithmetic means. The question answered by the authors is thus equivalent, as they recognize, to determining those \(p\), \(q\), \(r\), \(s\) for which \(M_{p}(M_{q}(x,y),M_{r}(x,y))=M_{s}(x,y)\). By means of examining a large number of cases, they offer the conclusion that all nontrivial solutions are given by \(p=s=0\), \(r=-q\), \(q\) arbitrary and by \(q=p\), \(r=0\) (or \(r=p\), \(q=0\)), \(s=p/2\), \(p\) arbitrary.