MAGIC SQUARES: WHEN THE METHOD FAILS

José Travassos Ichihara, Patricia Nunes da Silva, Renata Cardoso Pires de Abreu

Abstract


http://dx.doi.org/10.5902/2179460X14642

In this article, we discuss the behavior of the solutions of a system of linear congruences related to the uniform step method. This is a method for constructing magic squares of odd order proposed and mathematically analyzed by Lehmer (1929). His analysis has several steps. In the first, involving the discussion of necessary and sufficient conditions for filling the square, Lehmer says that if two numbers keep a certain relationship to each other, they will be designated to occupy the same cell of the square. We conclude here that numbers that fulfill the mentioned relationship never occupy the same cell. In other words, what Lehmer says is not true.


Keywords


Quadrados mágicos. Congruências. Método do passo uniforme.



DOI: http://dx.doi.org/10.5902/2179460X14642

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