Abstract

AbstractLet be a positive integer, be a magic square, where . is called most perfect magic square (MPMS for short) if , and . Let , where . is called rational if both and possess the property that the sums of the numbers in every row and every column are the same; otherwise, is said to be irrational. It was shown that there exists an MPMS if and only if and . In this paper, it is proved that there exists an irrational MPMS if and only if and .

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