数集构成4n阶泛对角线幻方的充分条件

SUFFICIENT CONDITION OF NUMBER SET CONSTRUCTING PANDIAGONAL MAGIC SQUARE OF ORDER 4n

本文以构造性方法证明:当8×2n^2型偏差分对称矩阵满足适当条件时,其元素之集可构成4n(n≥1)阶泛对角线幻方。构成二维等差矩阵的数集及由1,2,…,16n^2构成的数集仅是该种数集的特例。

This paper amis to establish a general method for pandiagonal magic square of order 4n. It is shown that when a8×2n^2 matrix A with symmetric partial difference in each direction satisfies d_1^(1) =d_3^(1),d_1^(2) =d_2^(2) = … =d_(2n^2-1)^(2) =d. Apandiagonal magic square of order 4n can always be constructed with elements of A. Number sets which consists of e1-ements of double equidfference matrix and natural numbers of series 1, 2, …, 16n^2 are special cases of the above condi-tion.