答案：2^16=65536
思路：在原式前面乘上（2-1）,从而不断地产生平方差,可以巧解.
(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 -1+1
=2^16=65536