Liang, Peiji; Sun, Rongguo; Ku, Tunghsin; Zhu, Lie A construction of addition-multiplication magic squares using orthogonal diagonal latin squares. (English) Zbl 0765.05025 J. Comb. Math. Comb. Comput. 11, 173-181 (1992). On page 489 of the joint book by the reviewer with A. D. Keedwell [Latin squares and their applications. Budapest: Akademiai Kiado (1974; Zbl 0283.05014)] one can find the following research problem: For what orders \(n\) do addition-multiplication magic squares exist? Solutions for some orders, namely 8,9,16 and certain odd orders, were known. In this paper the author uses orthogonal diagonal latin squares to show the existence of an addition-multiplication magic square of order \(mn\) for positive integers \(m\) and \(n\), where \(m\) and \(n\) are different from \(1,2,3\) and \(6\). Reviewer: József Dénes (Budapest) Cited in 3 Documents MSC: 05B15 Orthogonal arrays, Latin squares, Room squares Keywords:addition-multiplication magic squares; orthogonal diagonal latin squares Citations:Zbl 0283.05014 PDFBibTeX XMLCite \textit{P. Liang} et al., J. Comb. Math. Comb. Comput. 11, 173--181 (1992; Zbl 0765.05025)