Construction of Normal Bimagic Squares of Order 2u

作     者：Wen LI Feng-chu PAN Guang-zhou CHEN Wen LI;Feng-chu PAN;Guang-zhou CHEN

作者机构：School of ScienceXichang UniversityXichang 615000China School of Environment and ResourceXichang UniversityXichang 615000China Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal ControlSchool of Mathematics and Information ScienceHenan Normal UniversityXinxiang 453007China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2020年第36卷第4期

页      面：771-789页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This paper is supported by the National Natural Science Foundation of China(Nos.11871417,11501181) Science Foundation for Youths(Grant No.2014QK05) Ph.D.(Grant No.qd14140)of Henan Normal University 

主　　题：magic square bimagic square complementary pair multimagic square Latin square 

摘      要：An n×n matrix A consisting of nonnegative integers is a general magic square of order n if thesum of elements in each row,column,and main diagonal is the same.A general magic square A of order n iscalled a magic square,denoted by MS(n),if the entries of A are distinct.A magic square A of order n is normalif the entries of A are n^2 consecutive *** A^*d denote the matrix obtained by raising each elementof A to the d-th *** matrix A is a d-multimagic square,dcnoted by MS(n,d),if A^*e is an MS(n)for 1≤e≤*** this paper we investigate the existence of normal bimagic squares of order 2u and prove that thereexists a normal bimagic square of order 2u,where u and 6 are coprime and u≥5.