(2-1)(2+1)(2^2+1)(2^4+1)…(2^32+1)+1 结果的个位数字是什么?
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(2-1)(2+1)(2^2+1)(2^4+1)…(2^32+1)+1 结果的个位数字是什么?
=(2^2-1)(2^2+1)(2^4+1)………………
=(2^4-1)(2^4+1)(2^8+1)…………
……
……
=(2^64-1)+1
=2^64
2末尾是2
2*2末尾是4
2*2*2末尾是8
2*2*2*2末尾是6
4个次方重复一次
64/4=16
末尾是6
(2-1)(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^4-1))(2^4+1)…(2^32+1)+1
=...
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
=1.844674407371e+019
(2-1)(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^4-1)(2^4+1)…(2^32+1)+1
=......
=(2^32-1)(2^32+1)+1
=(2^64-1)+1
=2^64
=2^(4*16)
=(2^4)^16
...
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(2-1)(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^4-1)(2^4+1)…(2^32+1)+1
=......
=(2^32-1)(2^32+1)+1
=(2^64-1)+1
=2^64
=2^(4*16)
=(2^4)^16
=16^16
6*6=36
所以不管6的几次方个位均为6
所以2^64 =16^16的个位数为6
收起
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