За векторното пространство на магическите квадрати от четвърти ред (в занимателната математика)
About the Vector Space of the Fourth Order Magic Squares (in Recreational Mathematics)

Summary/Abstract: In the present study a more general (than the traditional) definition of the term magic squares of the fourth order is adopted and sufficient conditions for their existence are indicated. Essential vector-algebraic properties of the fourth-order magic squares have been studied by elementary means of linear algebra. A direct proof of the theorem for the dimensionality of their vector space is made, without using the more general theorem for the dimensionality of the vector space of the magic squares of order n (n ≥3). By solving a linear system of 10 linear equations with 17 unknowns, it is shown that when compiling a fourth-order magic square (in the general case), eight (of the sixteen) coordinates can be given arbitrarily. There are two formulated and solved problems which corroborate the propositional. The present paper is meant for some lessons in recreational mathematics.

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