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

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 00:35:39

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

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

将第一个式子变形为(2的2次方)-1;再依次用平方差公式就可以了。2的64次方