求(2+1)(2^2+1)(2^4+1).(2^64+1)+1的末尾数
4个回答

(2+1).(2^2+1).(2^4+1).(2^64+1)+1

=(2-1)(2+1).(2^2+1).(2^4+1).(2^64+1)+1

=(2^2-1)(2^2+1).(2^4+1).(2^64+1)+1

=(2^4-1)(2^4+1).(2^64+1)+1

=(2^8-1).(2^64+1)+1

.

=(2^64-1)(2^64+1)+1

=2^128-1 +1

=2^128

2^1的末尾数是:2

2^2的末尾数是:4

2^3的末尾数是:8

2^4的末尾数是:6

2^5的末尾数是:2

.

2^n的末尾数是关于2,4,8,6循环

128/4=32

所以2^128的末尾数是:6

即(2+1)(2^2+1)(2^4+1).(2^64+1)+1的末尾数是:6