(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1))(2^32+1)+1的末位数字是?
问题描述:
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1))(2^32+1)+1的末位数字是?
答
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1))(2^32+1)+1
=(2-1)(2+1)(2^2+1)...(2^16+1)(2^32+1)+1
=(2^2-1)(2^2+1)...(2^32+1)+1
=...
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64
2^n的个位是以:2、4、8、6循环
64/4=16
没有余数,说明个位是:6