Giúp em chứng minh tính chia hết với ạ

`a)`

`13 . 12 + 26 . 27`

`= 13 . 12 + 13 . 2 . 27`

`= 13 . (12 + 2 . 27)`

`= 13 . (12 + 54)`

`= 13 . 66`

`= 13 . 2 . 66 \vdots 13 . 33`

`=> 13 . 12 + 26 . 27 \vdots 13 . 33` `(đpcm)`

`b)`

`6^5 . 5 - 3^5`

`= 2^5 . 3^5 . 5 - 3^5 . 1`

`= 3^5 . (2^5 . 5 - 1)`

`= 3^5 . (32 . 5 - 1)`

`= 3^5 . (160 - 1)`

`= 3^5 . 159`

`= 3^5 . 53 . 3 \vdots 53`

`=> 6^5 . 5 - 3^5 \vdots 53` `(đpcm)`

`c)`

`@` `TH_{1} :`

`2 + 2^2 + 2^3 + 2^4 + ... + 2^120`

`= (2 + 2^2) + (2^3 + 2^4) + ... + (2^119 + 2^120)`

`= 3 . 2 + 3 . 2^2 + ... + 3 . 2^119`

`= 3 . (2 + 2^2 + 2^119) \vdots 3`

`=> 2 + 2^2 + 2^3 + 2^4 + ... + 2^120 \vdots 3` `(đpcm)`

`@` `TH_{2} :`

`2 + 2^2 + 2^3 + 2^4 + ... + 2^120`

`= (2 + 2^2 + 2^3) + (2^4 + 2^5 + 2^6) + ... + (2^118 + 2^119 + 2^120)`

`= 2 . (1 + 2 + 2^2) + 2^4 . (1 + 2 + 2^2) + ... + 2^118 . (1 + 2 + 2^2)`

`= 2 . 7 + 2^4 . 7 + ... + 2^118 . 7`

`= (2 + 2^4 + ... + 2^118) . 7 \vdots 7`

`=> 2 + 2^2 + 2^3 + 2^4 + ... + 2^120 \vdots 7` `(đpcm)`

`@` `TH_{3} :`

`2 + 2^2 + 2^3 + 2^4 + ... + 2^120`

`= (2 + 2^2 + 2^3 + 2^4 + 2^5) + ... + (2^116 + 2^117 + 2^118 + 2^119 + 2^120)`

`= 2 . (1 + 2^2 + 2^3 + 2^4) + ... + 2^116 . (1 + 2^2 + 2^3 + 2^4)`

`= 2 . 31 + .. + 2^116 . 31`

`= (2 + ... + 2^11) . 32 \vdots 31`

`=> 2 + 2^2 + 2^3 + 2^4 + ... + 2^120 \vdots 31` `(đpcm)`

`@` `TH_{4} :`

`2 + 2^2 + 2^3 + 2^4 + ... + 2^120`

`= (2 + 2^5) + (2^2 + 2^6) + ... + (2^116 + 2^120)`

`= 2 . (1 + 16) + 2^2 . (1 + 16) + ... + 2^116 . (1 + 16)`

`= 2 . 17 + 2^2 . 17 + ... + 2^116 . 17`

`= 2 . (2 + 2^2 + ... + 2^116) \vdots 17`

`=> 2 + 2^2 + 2^3 + 2^4 + ... + 2^120 \vdots 17` `(đpcm)`