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Magic cubes and Prouhet sequences. (English) Zbl 0389.05018

A magic \(N\)-cube of order \(T\) is an \(N\)-dimensional cubical arrangement of the numbers \(1,2,\dots,T^N\) such that the sum of the numbers on any line parallel to an edge or on a great diagonal is the same. In this paper a construction of a magic \(N\)-cube of order \(t^M\) is given that is valid whenever \(t\mid MN\) and either \(M\geq 2\) or \(t\) is odd. This construction is based on the \(t\)-ary Morse-Hedlund-Prouhet sequence, and has interesting connections with the Terry-Escott problem.
Reviewer: W. H. Mills

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares
11B83 Special sequences and polynomials
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