试说明:对于任何正整数n,2的n+4次方-2^n必能被3整除
人气:174 ℃ 时间:2019-08-21 08:44:21
解答
2^(n+4) - 2^n
=2^n * 2^4 - 2^n
=2^n (2^4-1)
=2^n(16-1)
=15 *2^n
=3 * 5 * 2^n
∴{ 2^(n+4) - 2^n } ÷ 3 = { 3 * 5 * 2^n } ÷ 3 = 5 * 2^n
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