Construction of Normal Bimagic Squares of Order 2u

• 作者: Wen LI Feng-chu PAN Guang-zhou CHEN
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 771-789
• 页数: 19页
• 语种: 英文

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 n2 consecutive integers.Let A*d denote 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*e is an MS(n)for 1≤e≤d.In this paper we investigate the existence of normal bimagic squares of order 2u and prove that there exists a normal bimagic square of order 2u,where u and 6 are coprime and u≥5.