Question

提问：试确定(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1的末位数字

过程

Answer 1

乘以(2-1)=1
则(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1
=(2^16-1)(2^16+1)(2^32+1)+1
=(2^32-1)(2^32+1)+1
=2^64
=(2^4)^16
=16^16

因为末位数字为6的无论多少次幂末位数字都是6
所以答案是末位数字为6

Answer 2

第2个是5，所有都是奇数，奇数*5是5，所以末位数是6