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不定方程x~2+y~2=z~2的正整数解叫做勾股数,记作(x,y,z),而当(x,y,z)不含有公约数时,则称之为基本勾股数,如(3,4,5),(5,12,13),(8,15,17)等。每一组基本勾股数与自然数相乘,结果仍得勾股数,如由基本勾股数(3,4,5)可以得到(6,8,10),(9,12,15),…以这些勾股数为边的直角三角形都是相似的。含有公约数的勾股数被称为可约勾股数。在研究勾股数的性质时,人们总是着眼于基本勾股数。在包罗一切勾股数的公式一: 中,当a,b同为奇数或同为偶数时,得出是可约
The positive integer solution of the indefinite equation x~2+y~2=z~2 is called the number of hooks, denoted as (x,y,z), and when (x,y,z) does not contain a common divisor, it is called The basic number of shares, such as (3,4,5), (5,12,13), (8,15,17) and so on. Each group of basic hook shares is multiplied by the natural number. The result is still the number of shares. If the number of basic shares (3,4,5) can be obtained (6,8,10), (9,12,15), ... The right-angled triangles with these hooks as edges are all similar. The number of argots containing a common divisor is called the number of guaranteable shares. When studying the nature of the number of hooks, people are always looking at the basic number of shares. In formula one that includes all the number of gouaches, when a and b are both odd or even, they are considered to be negotiable.