163 n^x+2n 能不能被3整除？ 1 x=3 2 n=5

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allennuli

11^#

发表于 2010-8-9 00:07:08 | 只看该作者

5^x+10=(6-1)^x+9+1

(6-1)^2=36-12+1
(6-1)^3=(36-12+1)(6-1)
.........
only the last number 1or -1 is not a multiple of 3,
when x is even, (-1)^x will be 1, then plus the last 1, 2 can not be divided by 3.
when x is odd, (-1)^x will be -1, then plus the last 1, equals 0. And all the order number will be multiple of 3. Thus it can be divided by 3.