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大家一见到3,4,5中的任意一个,就会脱口而出含有这个数的勾股数3,4,5。然而,碰到大于2的任意正整数时,也能做到脱口而出吗?要想做到这一点并不难,只要用本文的办法就行了。设M为所告诉的大于2的正整数。可据下列情况分别得勾股数: 一 M为偶数:M,(M~2-4)/4,(M~2+4)/4 二 M±1是完全平方数:2(M±1)~(1/2),M,M±2 三 M为奇数:M,(M~2-1)/2·((M~2+1)/2) 四 2M±1是完全平方数:(2M±1)~(1/2),M,M±1 这些公式的证明都极为简单,相信同学们自己能够很快证明出来。获得步骤:一、M的附近(M±1)是否有完全平
As soon as everybody sees any one of 3, 4, and 5, it will blurt out the number 3, 4, 5 of this number. However, when you come across any positive integer greater than 2, can you talk about it? It is not difficult to do this, just use the method of this article. Let M be a positive integer greater than 2 as told. The number of hooks can be obtained according to the following conditions: One M is an even number: M, (M~2-4)/4, (M~2+4)/4 Two M±1 is a complete square number: 2(M±1) )~(1/2), M, M±2 Three M is an odd number: M,(M~2-1)/2((M~2+1)/2) Four 2M±1 is a complete square number: (2M ± 1) ~ (1/2), M, M ± 1 The proof of these formulas is extremely simple, I believe that the students themselves can quickly prove it. Obtain the steps: 1. Is M near (M ± 1) completely flat?