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| 平方幻方专题 |
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平方幻方 | 中国幻方大世界 |
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“平方数”幻方 这以后，人们开始探讨最小的平方幻方问题了。已知的最小的平方幻方是8阶平方幻方（二次幻方）.
它是平方幻方中最小的吗?,Pfeffermann在1890年发现第一个8阶平方幻方后，他就想探讨神秘的7阶或更小的平方幻方。我们前面提到的法国数学作家Edouard
卢卡斯，他在这本半月刊里，发表了两篇证明文章，他的结论是三阶、四阶平方幻方不存在，即使用非连续的数字三阶平方幻方也不会存在。
6阶“平方数”幻方 Unfortunately to late to be published in the M.I. article, I constructed, in June 2005, the first 6x6 magic squares of squares. If I am right, 6x6 magic squares of squares using squared consecutive integers (0² to 35², or 1² to 36²) are impossible. My 6x6 magic square of squares does NOT use squared consecutive integers... but it is interesting to see the used numbers:
It is impossible to construct a 6x6 magic square of squares with a smaller magic sum. But it is possible to construct other samples with the same magic sum S2 = 2551, or with other bigger sums.
An interesting supplemental characteristics of this sample: the 3 smallest integers (0², 1², 2²) and the 2 biggest (35², 36²) are used together in the first row. 7阶“平方数”幻方 Unfortunately to late to be published in the M.I. article, I constructed, in June 2005, the first 7x7 magic squares of squares. The smallest order allowing magic squares of squares using squared consecutive integers is the order 7. An indirect consequence: the impossibility of 7x7 bimagic squares is not coming from a problem with its squared numbers! Here is my sample using the squared integers from 0² to 48²:
An interesting supplemental characteristics added in this sample: the 7 rows are magic (S1=168) when the integers are not squared, meaning that the 7 rows are bimagic!
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