一道简洁的数学证明题,自己想的求证:N^5-N=30K,(N,K∈Z)最好不用讨论分几种情况~下面是不用讨论的方法:发现 Y=(N-1)N(N+1)(N+2)(N+3)能被30整除,将其变形为(N-1)N(N+1)(N²+5N+6)=(N-1)N(N+1)(N²+1+
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![一道简洁的数学证明题,自己想的求证:N^5-N=30K,(N,K∈Z)最好不用讨论分几种情况~下面是不用讨论的方法:发现 Y=(N-1)N(N+1)(N+2)(N+3)能被30整除,将其变形为(N-1)N(N+1)(N²+5N+6)=(N-1)N(N+1)(N²+1+](/uploads/image/z/4250044-28-4.jpg?t=%E4%B8%80%E9%81%93%E7%AE%80%E6%B4%81%E7%9A%84%E6%95%B0%E5%AD%A6%E8%AF%81%E6%98%8E%E9%A2%98%2C%E8%87%AA%E5%B7%B1%E6%83%B3%E7%9A%84%E6%B1%82%E8%AF%81%EF%BC%9AN%5E5-N%3D30K%2C%28N%2CK%E2%88%88Z%EF%BC%89%E6%9C%80%E5%A5%BD%E4%B8%8D%E7%94%A8%E8%AE%A8%E8%AE%BA%E5%88%86%E5%87%A0%E7%A7%8D%E6%83%85%E5%86%B5%7E%E4%B8%8B%E9%9D%A2%E6%98%AF%E4%B8%8D%E7%94%A8%E8%AE%A8%E8%AE%BA%E7%9A%84%E6%96%B9%E6%B3%95%EF%BC%9A%E5%8F%91%E7%8E%B0+Y%3D%28N-1%29N%28N%2B1%29%28N%2B2%29%28N%2B3%29%E8%83%BD%E8%A2%AB30%E6%95%B4%E9%99%A4%EF%BC%8C%E5%B0%86%E5%85%B6%E5%8F%98%E5%BD%A2%E4%B8%BA%28N-1%29N%28N%2B1%29%28N%26sup2%3B%2B5N%2B6%29%3D%28N-1%29N%28N%2B1%29%28N%26sup2%3B%2B1%2B)
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