已知(2+1)(2^2+1)(2^4+1)(2^8+1)×…×(2^64+1)+1（1）计算结果.（2）判断结果的末尾数字是多少

Question

已知(2+1)(2^2+1)(2^4+1)(2^8+1)×…×(2^64+1)+1 （1）计算结果.（2）判断结果的末尾数字是多少

Answer 1

(2+1)(2^2+1)(2^4+1)(2^8+1)×…×(2^64+1)+1
=（2-1）(2+1)(2^2+1)(2^4+1)(2^8+1)×…×(2^64+1)+1
=(2^-1)(2^2+1)(2^4+1)(2^8+1)×…×(2^64+1)+1
=(2^4-1)(2^4+1)(2^8+1)×…×(2^64+1)+1
=..
=2^128-1
=2^128
2^1=2
2^2=4
2^3=8
2^4=16
2^5=32
2^6=64
所以尾数是 2 4 8 6 的循环
128÷4=32
所以尾数是6