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纵横图是中国古代数学家所发現的。它是指把n~2个連續自然数(特别是1,2,3,4,…,n~2)排列在正方形內,使各行、各列及各对角綫上的数目之和相等。如果略加修改为“把从1起的連續的n~2个自然数排列成方陣,使各行、各列及各对角綫上的数目之和全为素数”,这就成了一个頗为有趣的数論問題。不但如此,我們还可要求得更多一点;除上述条件外,还可使其符合“各行、各列及各对角綫上的数目的平方和全为素数”。符合这种条件的排列是否存在呢?答案是肯定的。下表中給出了从1到25为止的5~2个自然的数
The crossword map was discovered by ancient Chinese mathematicians. It refers to arranging n~2 consecutive natural numbers (especially 1,2,3,4,...,n~2) within a square so that the sum of the number of lines, columns, and diagonals is equal. If it is slightly modified to “arrange continuous n~2 natural numbers from 1 to a square matrix so that the sum of the number of lines, columns, and diagonals is a prime number”, this becomes quite interesting. Number theory problems. Not only that, we can ask for a little more; in addition to the above conditions, it can also be made to conform to the “square sum of the numbers of all rows, columns and diagonals is all prime”. Does the arrangement that meets this condition exist? The answer is yes. The following table shows 5 to 2 natural numbers from 1 to 25.