Adler, Allan; Li, Shuo-Yen Robert Magic cubes and Prouhet sequences. (English) Zbl 0389.05018 Am. Math. Mon. 84, 618-627 (1977). 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 Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 10 Documents MSC: 05B15 Orthogonal arrays, Latin squares, Room squares 11B83 Special sequences and polynomials Keywords:magic \(N\)-cube; Morse-Hedlund-Prouhet sequence; Terry-Escott problem PDF BibTeX XML Cite \textit{A. Adler} and \textit{S.-Y. R. Li}, Am. Math. Mon. 84, 618--627 (1977; Zbl 0389.05018) Full Text: DOI OpenURL