| 数集构成4n阶泛对角线幻方的充分条件 |
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| 引用本文： | 张世德 王际昭. 数集构成4n阶泛对角线幻方的充分条件[J]. 河南师范大学学报(自然科学版), 1990, 0(3): 70-73 |
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| 作者姓名： | 张世德 王际昭 |
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| 作者单位： | 河南师范大学数学系(张世德)，新乡市九中(王际昭) |
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| 摘 要： | 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。
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| 关 键 词： | 泛对角线幻方 二维等差矩阵 偏差分对称矩阵 |
SUFFICIENT CONDITION OF NUMBER SET CONSTRUCTING PANDIAGONAL MAGIC SQUARE OF ORDER 4n |
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| Zhang Shide,Wang Jizhao. SUFFICIENT CONDITION OF NUMBER SET CONSTRUCTING PANDIAGONAL MAGIC SQUARE OF ORDER 4n[J]. Journal of Henan Normal University(Natural Science), 1990, 0(3): 70-73 |
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| Authors: | Zhang Shide Wang Jizhao |
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| Affiliation: | Zhang Shide;Wang Jizhao Department of Mathematics Nmuber Ninth Middle School of Xin Xiang |
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| Abstract: | 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. |
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| Keywords: | pandiagonal magic square double equidifference matrix matrix with symmetric partial difference in each direction |
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