Question

[hồ minh khôi]

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

Answer 1

[Minh Triều]

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

=1.(2+1)(2²+1)(2⁴ +1)(2⁸+1)(2¹⁶+1) - 2³²

=(2-1).(2+1)(2²+1)(2⁴ +1)(2⁸+1)(2¹⁶+1) - 2³²

=(2²-1)(2²+1)(2⁴ +1)(2⁸+1)(2¹⁶+1) - 2³²

=(2⁴-1)(2⁴ +1)(2⁸+1)(2¹⁶+1) - 2³²

=(2⁸-1)(2⁸+1)(2¹⁶+1) - 2³²

=(2¹⁶-1)(2¹⁶+1) - 2³²

=2³²-1-2³²

=-1

Answer 2

[Trần Đức Thắng]

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

=  3 ( 2^2 + 1) ....( 2^16 + 1) -2^32

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

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

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

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

= 2^32 - 1 - 2^32

=-1