Question

(2+1)(2的平方+1)(2的四次方+1)..(2的64次方+1),结果为(2的128次方-1),用平方差公式算出来,

Answer 1

(2+1)(2^2+1)(2^4+1).(2^64+1)

=(2-1)(2+1)(2^2+1)(2^4+1).(2^64+1)

=((2^2-1)(2^2+1))(2^4+1).(2^64+1)

=(2^4-1)(2^4+1).(2^64+1)

.

=(2^64-1)(2^64+1)

=2^128-1