Ways of constructing optimal magic cube of order n when (n, 2·3·5·7)=1

Xiao-song Chen

doi:10.1007/s11771-002-0014-2

Journal of Central South University ›› 2002, Vol. 9 ›› Issue (1) : 70 -72. DOI: 10.1007/s11771-002-0014-2

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Ways of constructing optimal magic cube of order n when (n, 2·3·5·7)=1

Xiao-song Chen ¹

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Abstract

An optimal magic cube of order n is a magic cube whose row sums, column sums and oblique sums of 9n layers are n(n³ + 1)/2. The author proved that optimal magic cubes of order n may be constructed as long as n and 2, 3, 5, 7 are relatively prime, and a formula for making optimal magic cubes by using optimal Latin squares and optimal magic squares was given.

Keywords

optimal Latin square / optimal magic square / complete residue system

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Xiao-song Chen. Ways of constructing optimal magic cube of order n when (n, 2·3·5·7)=1. Journal of Central South University, 2002, 9(1): 70-72 DOI:10.1007/s11771-002-0014-2

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References

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