(a+1)(a^2+1)(a^4+1)……(a^64+1)=
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/17 17:53:50
(a+1)(a^2+1)(a^4+1)……(a^64+1)=
(a+1)(a^2+1)(a^4+1)……(a^64+1)=
(a+1)(a^2+1)(a^4+1)……(a^64+1)=
原式=(a-1)(a+1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^2-1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^4-1)(a^4+1)……(a^64+1)/(a-1)
反复用平方差
=(a^64-1)(a^64+1)/(a-1)
=(a^128-1)/(a-1)
(a128-1)/(a-1)
原式=(a-1)(a+1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^2-1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^4-1)(a^4+1)……(a^64+1)/(a-1)
=(a^64-1)(a^64+1)/(a-1)
=(a^128-1)/(a-1)
(a+1)(a^2+1)(a^4+1)……(a^64+1)
=(a-1)(a+1)(a^2+1)……(a^64+1)/(a-1)
=(a^2-1)(a^2+1)……(a^64+1)/(a-1)
=(a^4-1)*.....(a^64+1)/(a-1)
.........
=(a^64-1)(a^64+1)/(a-1)
=(a^128-1)/(a-1)
楼上的错了!当a=1时,原式=2^64
当a不等于0时,原式=(a-1)(a+1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^2-1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^4-1)(a^4+1)……(a^64+1)/(a-1)
=.....
=(a^64-1)(a^64+1)/(a-1)
=(a^128-1)/(a-1)
=(a^128-1)/(a-1)
原式=(a^3+a^2+a+1)(a^4+1)...
=(a^7+a^6+...+1)(a^8+1)...
...
=a^128+a^127+...+1
当a≠1时
原式
=(a-1)(a+1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^2-1)(a^2+1)(a^4+1)……(a^64+1)/(a-1)
=(a^4-1)(a^4+1)……(a^64+1)/(a-1)
=(a^128-1)/(a-1)
当a=1时
原式=2*2*2*2*2*2*2=128