(2^1+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^1+1)(2^2+1)(2^4+1)(2^8+1)×(2-1)+1
=(2²-1)×(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)×(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=2^16-1+1
=2^16
(2^1+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^1+1)(2^2+1)(2^4+1)(2^8+1)×(2-1)+1
=(2²-1)×(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)×(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=2^16-1+1
=2^16