CM `A \vdots 3`
Ta có:
`A = 2 + 2^2 + 2^3 + ..... + 2^59 + 2^60`
`= (2 + 2^2) + (2^3 + 2^4) + ..... + (2^59 + 2^60)`
`= 2 . (1 + 2) + 2^3 . (1 + 2) + ..... + 2^59 . (1 + 2)`
`= 2 . 3 + 2^3 . 3 + ..... + 2^59 . 3`
`= (2 + 2^3 + ...... + 2^59) . 3`
Vì `3 \vdots 3`
`⇒ (2 + 2^3 + ...... + 2^59) . 3 \vdots 3`
`⇒ A \vdots 3`.
CM `A \vdots 7`
Ta có:
`A = .....................`
`= (2 + 2^2 + 2^3) + ...... + (2^58 + 2^59 + 2^60)`
`= 2 . (1 + 2 + 2^2) + ....... + 2^58 . (1 + 2 + 2^2)`
`= 2 . 7 + ...... + 2^58 . 7`
`= (2 + ..... + 2^58) . 7`
`⇒ (2 + ..... + 2^58) . 7 \vdots 7`
`⇒ A \vdots 7`.
CM `A \vdots 15`
Ta có:
`A = ........................`
`= (2 + 2^2 + 2^3 + 2^4) + .......... + (2^57 + 2^58 + 2^59 + 2^60)`
`= 2 . (1 + 2 + 2^2 + 2^3) + ....... + 2^57 . (1 + 2 + 2^2 + 2^3)`
`= 2 . 15 + ....... + 2^57 . 15`
`= (2 + ....... + 2^57) . 15 \vdots 15`
`⇒ A \vdots 15`.
