(2+1)(2的平方+1)(2的4方+1)(2的8方+1)(2的16方+1)(2的32方+1)(2的64方+1)+1的末尾数字是?

题目

(2+1)(2的平方+1)(2的4方+1)(2的8方+1)(2的16方+1)(2的32方+1)(2的64方+1)+1的末尾数字是?
快

答案

(2+1)(2的平方+1)(2的4方+1)(2的8方+1)(2的16方+1)(2的32方+1)(2的64方+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^32-1)(2^32+1)(2^64+1)+1
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
2^1=2
2^2=4
2^3=8
2^4=16
2^5=32
.
2^n的尾数是关于2,4,8,6循环
128/4=32
所以2^128的末尾数字是：6