(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

(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
可以先求出前面乘积的未尾数字
2 2
2*2 4
2^4 6
2^8 6
2^16 6
2^32 6
2^64 6
加一之后乘起来
7^5*3*5
7 7
7^2 9
7^3 3
7^4 1
7^5 7
7*3*5+1
最后一位是
6

(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
=(2^2-1)(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
=2^128-1+1
=2^128
2^1=2 2^2=4 2^3=8 2^4=16 2^5=32 2^6=64....
128/4=32 所以末尾数字是6

(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