计算（2-1)(2+1)(2²+1)(2的四次方+1)(2的八次方+1)

来源：学生作业学帮网编辑：学帮网时间：2024/05/29 04:49:06

(x-y)(x+y)=x^2-y^2
(2-1)(2+1)=2^2-1
(2^2-1)(2^2+1)=2^4-1
(2^4-1)(2^4+1)=2^8-1
(2^8-1)(2^8+1)=2^16-1

2-1)(2+1)(2²+1)(2的四次方+1)(2的八次方+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

（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
=65535

原式＝1×3×5×17×257
＝65535
蓝木连