On the Existence of a Normal Trimagic Square of Order 16n
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 orde...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/8377200 |
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| _version_ | 1832553070116995072 |
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| author | Can Hu Jiake Meng Fengchu Pan Maoting Su Shuying Xiong |
| author_facet | Can Hu Jiake Meng Fengchu Pan Maoting Su Shuying Xiong |
| author_sort | Can Hu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-888c53b711c94a308857878d69b43c70 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-888c53b711c94a308857878d69b43c702025-02-03T05:57:03ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/8377200On the Existence of a Normal Trimagic Square of Order 16nCan Hu0Jiake Meng1Fengchu Pan2Maoting Su3Shuying Xiong4College of Mathematics and PhysicsCollege of Mathematics and PhysicsCollege of Mathematics and PhysicsCentre for Retired ManagersMeishan Vocational and Technical CollegeThe 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.http://dx.doi.org/10.1155/2023/8377200 |
| spellingShingle | Can Hu Jiake Meng Fengchu Pan Maoting Su Shuying Xiong On the Existence of a Normal Trimagic Square of Order 16n Journal of Mathematics |
| title | On the Existence of a Normal Trimagic Square of Order 16n |
| title_full | On the Existence of a Normal Trimagic Square of Order 16n |
| title_fullStr | On the Existence of a Normal Trimagic Square of Order 16n |
| title_full_unstemmed | On the Existence of a Normal Trimagic Square of Order 16n |
| title_short | On the Existence of a Normal Trimagic Square of Order 16n |
| title_sort | on the existence of a normal trimagic square of order 16n |
| url | http://dx.doi.org/10.1155/2023/8377200 |
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