Question

Prove the divisibility of the following numbers: 7^6+7^5−7^4 by 11

Answer 1

`7^6+7^5-7^4=7^4(7^2+7-1)=7^4(49+7-1)=7^4*55`

Since
`11|55`, it follows that
`11|7^6+7^5-7^4`.

Answer 2

7^4 * 5

Explanation:

7^6+7^5-7^4 = 7^4(7^2+7-1) = 7^4(55), 55/5 = 11, 7^4 * 5 = 55/5, 7^4 * 5 by 11