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[数论] 存在性证明5

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hbghlyj Posted 2019-7-27 22:24 |Read mode

存在无穷多素数n,使得$10^{n-1}+10^{n-2}+...+1$是合数

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Author| hbghlyj Posted 2019-7-27 22:37

Screenshot_2019_0726_183407(1).png

例如111=3×37,11111=41×271都是合数
相反地,易证:n是合数,则$10^{n-1}+...+1$是合数

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