非素数阶幻方的构造

基于矩阵运算,给出任意双偶数阶和非素数阶幻方的新构造方法:1)由任一低阶m(m为偶数且m≠2)幻方生成一高阶2m阶幻方;2)利用已知的m(m≠2)阶和n(n≠2)阶两个幻方,构造任意的非素数mn阶幻方,加强一些条件后,进一步提出构造两类高级幻方(泛对角线幻方和关联幻方)的新方法.

The Constructing Method of Magic Square with Non-Prime Order

Two elegant methods for constructing magic squares of even order(singly even or doubly even)will be firstly will be introduced.By this method,a lager mount of magic squares with wonderful features can be obtained.Furthermore,we also give a new method of constructing two types of advanced magic squares(pan-magic squares or associative magic squares)with mn-order by one m-order magic square and another n-order magic square,where m≠2,n≠2.