作业帮(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 07:19:16
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),
题没有打完
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2²-1) (2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),/3+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),/3+1
=...
=(2^128-1)/3 +1
先乘以(2²-1),再除以3,保证相等
然后反复应用平方差公式
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=（2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1)
=...
=(2^128-1)/3
[(2^2-1)× (2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1]/(2^2-1)
=[(2^4-1)2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^16-1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^32-1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^64-1)(2^64+1)]/(2^2-1)
=(2^128-1)/3
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=（2^2-1）(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1）
= (2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1）
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1）
=………………
=（2^128-1）/（2^2-1）
=1.13^38(或=（2^128-1）/3)
比如用(2^2-1)去乘(2^2+1) 用(2^4-1)去乘(2^4+1)…以此类推,再除掉所乘的数.原理一样,但更容易做(个人认为)