a) `8^9 - 2^24`
`= (2^3)^9 - 2^24`
`= 2^27 - 2^24`
`= 2^24 ( 2^3 -1)`
`= 2^24 . (8-1)`
`= 2^24 .7 vdots 7` và `2^24 .7 vdots 2`
Mà `(2;7)=1`
`=> 8^9 - 2^21 vdots 14`
Vậy `8^9 - 2^21 vdots 14`
b) `2^2020 - (2^0 + 2^1 + ...+ 2^2018+ 2^2019)`
Đặt `A= 2^0 + 2^1 + ...+ 2^2018+ 2^2019`
`2A= 2( 2^0 + 2^1 + ...+ 2^2018+ 2^2019)`
`2A= 2 + 2^2 + ...+ 2^2019 + 2^2020`
`2A -A = 2+ 2^2 + ...+ 2^2019 + 2^2020 - 2^0 - 2^1 -...-2^2018 - 2^2019`
`A= 2^2020 - 2^0`
`A= 2^2020 -1`
`=> 2^2020 - (2^0 + 2^1 + ...+ 2^2018) + 2^2019) = 2^2020 - (2^2020 -1)`
`= 2^2020 -2^2020 +1`
`= 1`
Vậy `2^2020 - (2^0 + 2^1 + ...+ 2^2018 + 2^2019) =1`
