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求证:N=(5^2)*(3^2n+1)*(2^n)-(3^n)*(6^n+2)能被13整除
人气:454 ℃ 时间:2020-05-13 17:17:26
解答
N=(5^2)*(3^2n+1)*(2^n)-(3^n)*(6^n+2)
=25*3^(2n+1)*2^n-3^n*2^(n+2)*3^(n+2)
=3^(2n+1)*2^n(25-3*2^2)
=3^(2n+1)*13
所以能被13整除
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