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A construction of addition-multiplication magic squares using orthogonal diagonal latin squares. (English) Zbl 0765.05025

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 \(6\).

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares

Citations:

Zbl 0283.05014
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