Toán chứng minh 125^7 – 25^9 chia hết cho 124 15/07/2021 By Amara chứng minh 125^7 – 25^9 chia hết cho 124
– Ta có : `125^7 – 25^9` `= (5^3)^7 – (5^2)^9` `= 5^(3.7) – 5^(2.9)` `= 5^21 – 5^18` `= 5^18. 5^3 – 5^18` `= 5^18. (5^3 – 1)` `= 5^18. (125 – 1)` `= 5^18. 124` – Ta lại có : `124 vdots 124` `=> 5^18. 124 vdots 124` `=> 125^7 – 25^9 vdots 124` Trả lời
$125^7-25^9$ $=(5^3)^7-(5^2)^9$ $=5^{21}-5^{18}$ $=5^{18}.5^3-5^{18}$ $=5^{18}.(5^3-1)$ $=5^{18}.(125-1)=5^{18}.124$ Vì $124.n\vdots 124$ $→5^{18}.124\vdots 124$ Vậy $125^7-25^9\vdots 124$ Trả lời
– Ta có :
`125^7 – 25^9`
`= (5^3)^7 – (5^2)^9`
`= 5^(3.7) – 5^(2.9)`
`= 5^21 – 5^18`
`= 5^18. 5^3 – 5^18`
`= 5^18. (5^3 – 1)`
`= 5^18. (125 – 1)`
`= 5^18. 124`
– Ta lại có : `124 vdots 124`
`=> 5^18. 124 vdots 124`
`=> 125^7 – 25^9 vdots 124`
$125^7-25^9$
$=(5^3)^7-(5^2)^9$
$=5^{21}-5^{18}$
$=5^{18}.5^3-5^{18}$
$=5^{18}.(5^3-1)$
$=5^{18}.(125-1)=5^{18}.124$
Vì $124.n\vdots 124$
$→5^{18}.124\vdots 124$
Vậy $125^7-25^9\vdots 124$