Question

一道数学题：（2+1）*(2的4次方+1)*（2的8次方+1）*（2的16次方+1）*（2的32次方+1）+1

Answer 1

题目好像抄漏了2^2+1项.

(2+1)(2^2+1)(2^4+1)（2^8+1）（2^16+1）（2^32+1）+1

=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1

=(2^8-1)(2^8+1)(2^16+1)(2^32+1)+1

=(2^16-1)(2^16+1)(2^32+1)+1

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

=2^64-1+1

=2^64