(2+1)(2^2+1)(2^4+1)(2^8+1)如何用平方差公式解?
问题描述：
(2+1)(2^2+1)(2^4+1)(2^8+1)如何用平方差公式解?
答
(2+1)(2^2+1)(2^4+1)(2^8+1)……（2^64+1)+1 =1*(2+1)(2^2+1)(2^4+1)(2^8+1)=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)=(2^2-1)(2^2+1)(2^4+1)(2^8+1) =(2^4-1)(2^4+1)(2^8+1)=(2^8-1)(2^8+1)=2^16-1