Question

计算：（2+1）（2^2+1）（2^4+1）（2^8+1）=_____.结果用幂的形式来表示

Answer 1

(2+1)(2^2+1)(2^4+1)(2^8+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