# Magične kocke i 3-adska zeta funkcija

Zovko, Iva (2015) Magične kocke i 3-adska zeta funkcija. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

Magic squares and cubes turned up throughout history, not only in mathematical context, but also in philosophical and religious contexts. According to a legend, the first magic square was discovered in China around 2800. BC. Despite the fact that magic $N$-cubes have been studied for a long time, they are still the subject of many research projects. We define magic square as square array of distinct integers $1, 2, \dots , M^2$ arranged such that the sum of $M$ numbers in any horizontal, vertical or main diagonal line is always the same number, known as magic constant. Magic $N$-cube is $N$-dimensional generalization of magic square whose magical constant is calculated by the following formula $S = \frac{M(M^N +1)}{2}$. Although there are many different methods, they can be divided into two groups: construction of magic $N$-cube of even order and construction of magic $N$-cube of odd order. We've explained two methods for constructing magic $N$-cube of odd order. The first one is Loubére method and the second one is technique of borders. Magic $N$-cubes of even order are classified into doubly even (n divisible by four) and singly even (n even, but not divisible by four). We've mentioned method using Prohuet series. This method is used for constructing magic $N$-cubes of doubly even order. In the end, we've defined multiplication of magic squares and explained which structure they form.