`a)` - Ta có :
`A = 2+ 2^2 + 2^3 + 2^4 + ... + 2^10`
`A = (2 + 2^2) + (2^3 + 2^4) + ... + (2^9 + 2^10)`
`A = 6 + 2^2. (2 + 2^2) + ... + 2^8.(2 + 2^2)`
`A = 6 + 2^2. 6 + ... + 2^8. 6`
`A = 6. (1 + 2^2 + ... + 2^8)`
- Ta lại có : `6 vdots 3`
`=> 6. (1 + 2^2 + ... + 2^8) vdots 3`
`=> A vdots 3`
`b)` - Ta có :
`A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^10`
`A = (2 + 2^2 + 2^3 + 2^4 + 2^5) + (2^6 + 2^7 + 2^8 + 2^9 + 2^10)`
`A = (2 + 4 + 8 + 16 + 32) + 2^5. (2 + 2^2 + 2^3 + 2^4 + 2^5)`
`A = 62 + 2^5. 62`
`A = 62. (1 + 2^5)`
- Ta lại có : `62 vdots 31`
`=> 62. (1 + 2^5) vdots 31`
`=> A vdots 31`
