(2+1)(2^2+1)(2^4+1)……(2^64+1)+1
=1*(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的末位數(shù)字：2
2^2的末位數(shù)字：4
2^3的末位數(shù)字：8
2^4的末位數(shù)字：6
2^5的末位數(shù)字：2
.
2^n的末位數(shù)字是關(guān)于2,4,8,6循環(huán)
128/4=32
所以2^128的末位數(shù)字是：6
即(2+1)(2^2+1)(2^4+1)……(2^64+1)+1的末位數(shù)字：6