(a+1)(a^2+1)(a^4+1)……(a^64+1)=
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(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