Question

(2+1）×（2的平方+1）×（2的四次方+1）×（2的8次方+1）×（2的16次方+1）×（2的32次方+1）+1=?

Answer 1

整个方程乘以（2-1）

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

平方差定理

=(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