A magic square is an n × n array of numbers whose rows, columns, and the two diagonals sum to μ. A regular magic square satisfies the condition that the entries symmetrically placed with respect to the center sum to 2μ. Using circulant matrices we describe a construction of regular classical magic squares that are nonsingular for all odd orders. A similar construction is given that produces regular classical magic squares that are singular for odd composite orders. This paper is an extension of [3].
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