cho M= $125^{7}$ – $625^{5}$ – $25^{9}$ Chứng minh: M chia hết cho 99

Ta có :

`M = 125^7 – 625^5 – 25^9`

`⇔ M = ( 5^3 )^7 – ( 5^4 )^5 – ( 5^2 )^9`

`⇔ M = 5^21 – 5^20 – 5^18`

`⇔ M = 5^18 . ( 5^3 – 5^2 – 1 )`

`⇔ M = 5^18 . 99`

`⇔ M = 5^18 . 9 . 11`

`⇔ M ⋮ 9`

`⇒ ĐPCM`