Ta có: `2^(2n).(2^(2n+1)-1)-1`
`=2^(2n). 2^(2n+1)-2^(2n)-1`
`=2^(2n+2n+1)-2^(2n)-1`
`=2^(4n+1)-2^(2n)-1`
`=2.(2^(2n))^2-2^(2n)-1`
`=2.(2^(2n))^2+2^(2n)-2.2^(2n)-1`
`=2^(2n)(2.2^(2n)+1)-(2.2^(2n)+1)`
`=(2.2^(2n)+1)(2^(2n)-1)`
`=(2^(2n+1)+1)(2^(2n)-1)`
Do `2^(2n+1)` chia 3 dư 2; `2^(2n)` chia 3 dư 1
`=> 2^(2n+1)+1 \vdots 3` và `2^(2n-1)-1 \vdots 3`
`-> (2^(2n+1)+1)(4^n-1) \vdots 9`
`-> (\text{đpcm})`