Behavior of powers of odd ordered special circulant magic squares

被引：5

作者：

Rani, Narbda ^{[1
]}

Mishra, Vinod ^{[1
]}

机构：

[1] St Longowal Inst Engn & Technol, Dept Math, Longowal, Punjab, India

来源：

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY | 2022年 / 53卷 / 04期

关键词：

Magic square; circulant magic squares; magic constant; matrix powers; singularity; mathematical induction;

D O I：

10.1080/0020739X.2021.1890846

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

This paper contains interesting facts regarding the powers of odd ordered special circulant magic squares along with their magic constants. It is shown that we always obtain circulant semi-magic square and special circulant magic square in the case of even and odd positive integer powers of these magic squares respectively. These magic squares will also take a particular form in the case of both even and odd positive integer powers. Moreover, they are singular under some conditions.

引用

页码：1044 / 1062

页数：19

共 25 条

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Liu, T
ACTA ARITHMETICA, 2004, 115 (02) : 97 - 118
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[24] MAGIC MOORE-PENROSE INVERSES AND PHILATELIC MAGIC SQUARES WITH SPECIAL EMPHASIS ON THE DANIELS-ZLOBEC MAGIC SQUARE
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[25] MAGIC MOORE-PENROSE INVERSES AND PHILATELIC MAGIC SQUARES WITH SPECIAL EMPHASIS ON THE DANIELS-ZLOBEC MAGIC SQUARE
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Drury, S. W.
Styan, George P. H.
Trenkler, Goetz
CROATIAN OPERATIONAL RESEARCH REVIEW, 2011, 2 (01) : 4 - 13

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