The existence of irrational most perfect magic squares
Jingyuan Chen, Jinwei Wu, Dianhua Wu · Journal of Combinatorial Designs · 2022
Abstract Let 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 .