数集构成奇数阶幻方的充分条件

关于幻方的构造,文讨论了由1、 2、…、n~2构造幻方的问题。本文证明构成2n+1(n≥1) 阶偏差分对称方阵的数集均可构成2n+1阶幻方,且对3阶幻方条件是充要的.满足这一条件的数集相当宽广,构成二维等差方阵的数集及1、 2、…、n~2组成的数集仅是构成偏差分对称方阵数集的特殊情况.偶数阶情况见文.

SUFFICIENT CONDITION OF NUMBER SET CONSTRUCTING MAGIC SQUARE OF ORDER ODD

On the construction of the magic squares.Fu Xiru.Shi Youmin Li Li.Wang Jizhao and the author gave distinct constructive methods.These articles only discussed how to construct magic square from 1,2,……,n~2. In this paper we prove a set of number forming a square matrix of the order 2n+1(n≥1) with symmetric partial difference in each direction can be used to construct a magic square of order 2n+1. When n=1,the condition is also necessary in order to construct a magic square of order 3. Number sets satisfying this condition are not rare.Number sets consisting of two dimen- sional double equidifferene matrix and(1、 2、 ……、n~2) are their special case.As for magic squares of order even we can know from wang Li(?)in and the author.