On the Existence of a Normal Trimagic Square of Order 16n

Can Hu, Jiake Meng, Fengchu Pan, Maoting Su, Shuying Xiong and Kenan Yildirim

Journal of Mathematics, 2023, vol. 2023, 1-9

Abstract: The study of magic squares has a long history, and magic squares have been applied to many mathematical fields. In this paper, we give a complete solution to the existence of normal trimagic squares of all orders 16n. In particular, we obtain a unified solution for the normal trimagic square of order 16n for n>3 by means of set partitions, semibimagic squares, Latin squares, and new product construction. Since there exist normal trimagic squares of orders 16, 32, and 48, we prove that there exists a normal trimagic square of order 16n for every positive integer n.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8377200

DOI: 10.1155/2023/8377200

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