思路：在原式乘上（2-1）,不断的产生平方差,可以巧解.(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1) 原式=(2-1)(2^1+1)(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...