Question

一道关于巧算的数学题`（1）.（2+1）（2方+1）（2的4次方+1）（2的8次方+1）+1 （2）.2006/（200

Answer 1

(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

2006/(2006^2-2555*2007)

=2006/(2006^2-(2006-1)*(2006+1))

=2006/(2006^2-(2006^2-1))

=2006/1

=2006