\(7^6+7^5-7^4\)
\(=7^4.\left(7^2+7-1\right)\)
\(=7^4.49+7-1\)
\(=7^4.5.11⋮11\)
Vậy \(7^6+7^5-7^4⋮11\)
Ta có: 7^6 + 7^5 - 7^4
= 7^4 . 7^2 + 7^4 . 7 - 7^4 . 1
= 7^4 . (7^2 + 7 - 1)
= 7^4 . (49 + 7 - 1)
= 7^4 . 55
= 7^4 . 5 . 11
Vì 7^4 . 5 . 11 chia hết cho 11
nên 7^6 + 7^5 - 7^4 chia hết cho 11