求(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1)+1 的个位数字
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求(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1)+1 的个位数字
求(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1)+1 的个位数字
求(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1)+1 的个位数字
(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)……(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)...(2^32+1)+1
=...
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
2的连续次幂,个位数字为
2,4,8,6循环,每组4个
64÷4=16
所以2^64的个位数字为6
即所求的个位数字为6
(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16...
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(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
2^1=2,个位数字为2
2^2=4,个位数字为4
2^3=8,个位数字为8
2^4=16,个位数字为6
2^5=32,个位数字为2
…………
规律:指数从1开始,每4个一组,按2,4,8,6循环。
64/4=16
2^64的个位数字是6
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