A = 51^n + 47^102 (n thuộc N ) Cm: A chia hết 10

`51^n + 47^(102)`

`= \overline{.....1} + 47^(100) * 47^2`

 `= \overline{.....1}  (47^4)^25 * \overline{(....1)} `

`=  \overline{.....1} * \overline{(....1)} * \overline{(....9)}`

`= \overline{....1} + \overline{...9}`

`= \overline{...0}` 

Vì `0 vdots 10` nên `A vdots 10 ` 

`A=51^n + 47^102`

Có `51^n=(\overline{...1})`

    `47^102=(47^2)^51=(\overline{...9})^51=(\overline{...9})^48.(\overline{...9})^3=(\overline{...9})^(4.12).(\overline{...9})=(\overline{...1}).(\overline{...9})=(\overline{...9})`

`A=(\overline{...1})+(\overline{...9})=(\overline{...0})`

⇒ `A\vdots10`