Chứng tỏ rằng: A = 2 +2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10+2^11+2^12 chia hết cho 7.

Question

giangnguyen · Answer

`A = 2 +2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^(10)+2^(11)+2^(12)`

`=(2+2^2+2^3)+(2^4+2^5+2^6)+(2^7+2^8+2^9)+(2^(10)+2^(11)+2^(12))`

`=2.(1+2+2^2)+2^4.(1+2+2^2)+2^7.(1+2+2^2)+2^(10).(1+2+2^2)`

`= 2.7+2^4 .7+2^7 .7+2^(10).7`

`=7.(2+2^4+2^7+2^(10))\vdots7`

`=>A\vdots7`

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