cho M= $125^{7}$ – $625^{5}$ – $25^{9}$ Chứng minh: M chia hết cho 99 02/07/2021 Bởi Ariana 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` Bình luận
M= $125^7 – 625^5 – 25^9$ $(5^3)^7 – (5^4)5 – (5²)^9$ $5^{21} – 5^{20} – 5^{18}$ $5^{18}(5^3-5^2 – 1)$ $5^{18}(125 – 25 -1)$ $5^{18}. 99$ ⇒ M chia hết cho 99 Bình luận
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`
M= $125^7 – 625^5 – 25^9$
$(5^3)^7 – (5^4)5 – (5²)^9$
$5^{21} – 5^{20} – 5^{18}$
$5^{18}(5^3-5^2 – 1)$
$5^{18}(125 – 25 -1)$
$5^{18}. 99$
⇒ M chia hết cho 99