劳保用品三指钢丝手套:一道数学问题
来源:百度文库 编辑:高校问答 时间:2024/05/25 22:28:48
(2+1)(2^2+1)(2^4+1)(2^8+1)+1=?
请把过程和结果写出来,我奖励50分!
请把过程和结果写出来,我奖励50分!
(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=2^16
=65536
2^16
过程:
原式=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=2^16-1+1
=2^16
(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=3*5*17*257+1
=65536
(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=3*5*17*257+1
=65536