Question

计算:(2+1)(2的平方+1)(2的4次方+1)(2d的8次方+1）（2的16次方+1)(2的32次方+1）

Answer 1

(2+1)(2^2+1)(2^4+1)...(2^32+1) 【2^2是2的2次方,2^4是2的4次方,其他则以此类推】

=(2-1)(2+1)(2^2+1)(2^4+1)...(2^32+1)

=(2^2-1)(2^2+1)(2^4+1）...（2^32+1)

=(2^4-1)(2^4+1)...(2^32+1)

=...

=(2^32-1)(2^32+1)

=2^64-1