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

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

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.

Suggested Citation

  • Can Hu & Jiake Meng & Fengchu Pan & Maoting Su & Shuying Xiong & Kenan Yildirim, 2023. "On the Existence of a Normal Trimagic Square of Order 16n," Journal of Mathematics, Hindawi, vol. 2023, pages 1-9, November.
    • Handle: RePEc:hin:jjmath:8377200
    DOI: 10.1155/2023/8377200
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    Cited by:

    1. Can Hu & Fengchu Pan, 2024. "New Infinite Classes for Normal Trimagic Squares of Even Orders Using Row–Square Magic Rectangles," Mathematics, MDPI, vol. 12(8), pages 1-17, April.

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