我们知道m>n,m、n都是正整数时,m2-n2、2mn、m2+n2为一组勾股数,当k为正整数时,用k乘以上各数,也可以得出另一组勾股数:k(m2-n2)、2kmn、k(m2+n2).如图1,若设过长方体一个顶点的三条棱长分别为a、b、c,长方体对角线的长为d.则a2+b2+c2=d2.下面我们就探索a、b、c、d都为正整数的构造方法,暂称这四 When we know that m>n, m and n are all positive integers, m2-n2, 2mn, and m2+n2 are the number of hooks. When k is a positive integer, multiplying k by the number above, we can also find another. The number of group of hooks: k(m2-n2), 2kmn, k(m2+n2). As shown in Fig. 1, if the lengths of the three edges of a vertex of the rectangular parallelepiped are a, b, and c, the length of the diagonal of the box is d. Then a2+b2+c2=d2. Let’s explore the construction method that a, b, c, and d are all positive integers. Let’s tentatively call this four.