Construction of Normal Bimagic Squares of Order 2u

被引：0

作者：

Wen LI ^{[1
]}

Feng-chu PAN ^{[2
]}

Guang-zhou CHEN ^{[3
]}

机构：

[1] School of Science, Xichang University

[2] School of Environment and Resource, Xichang University

[3] Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Science, Henan Normal University

来源：

Acta Mathematicae Applicatae Sinica | 2020年 / 36卷 / 04期

基金：

中国国家自然科学基金;

关键词：

D O I：

暂无

中图分类号：

O151.21 [矩阵论];

学科分类号：

070104 ;

摘要：

An n × n matrix A consisting of nonnegative integers is a general magic square of order n if the sum of elements in each row, column, and main diagonal is the same. A general magic square A of order n is called a magic square, denoted by MS（n）, if the entries of A are distinct. A magic square A of order n is normal if the entries of A are n;consecutive integers. Let A*ddenote the matrix obtained by raising each element of A to the d-th power. The matrix A is a d-multimagic square, denoted by MS（n, d）, if A;is an MS（n） for 1 ≤ e ≤ d. In this paper we investigate the existence of normal bimagic squares of order 2 u and prove that there exists a normal bimagic square of order 2u, where u and 6 are coprime and u ≥ 5.

引用

页码：771 / 789

页数：19

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