计算(2+1)*(2^2+1)*(2^4+1)*(2^8+1)*(2^16+1)*(2^32+1)+1

来源:学生作业学帮网 编辑:学帮网 时间:2024/07/04 12:35:39

计算(2+1)*(2^2+1)*(2^4+1)*(2^8+1)*(2^16+1)*(2^32+1)+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
=2^64-1+1
=2^64

=(2^2-1)*(2^2+1)*(2^4+1)*(2^8+1)*(2^16+1)*(2^32+1)+1
=2^23

(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)*(2^4+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
=2^64-1+1=2^64

(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)*(2^4+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
=2^64-1+1=2^64

(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)*(2^4+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
=2^64-1+1=2^64