当n是正整数时,5的2次方*3的2n+1次方*2的n次方-3的n次方*6的n-2次方是13的倍数吗
人气:156 ℃ 时间:2020-02-04 22:14:58
解答
楼上的答案太牵强了,maybe n为其他数的时候可以(即使他的答案确实是对的)
5^2* 3^(2n+1)* 2^n -3^n *6^(n-2)
=5^2* 3^(2n+1)* 2^n -3^(2n-2) *2^(n-2)
=3^(2n-2) *2^(n-2)(5^2* 3^3* 2^2-1)
=3^(2n-2) *2^(n-2)*(2700-1)
=3^(2n-2) *2^(n-2)*2699
2699/13=207余8
所以他并不是13的倍数
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