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