Question

用简便方法计算（2+1）x（2X2+1）x（2的四次幂+1）x（2的八次幂+1）+1

Answer 1

利用平方差公式

(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

=65536-1

=65535