Prove the divisibility of the following numbers: 7^6+7^5−7^4 by 11 Question Prove the divisibility of the following numbers: 7^6+7^5−7^4 by 11 in progress 0 Math 3 months 2022-02-15T10:18:44+00:00 2022-02-15T10:18:44+00:00 1 Answer 0 views 0

## Answers ( )

7^6 + 7^5 – 7^4 = 7^4*7^2 + 7^4*7^1 – 7^4*1

7^6 + 7^5 – 7^4 = 7^4(7^2 + 7^1 – 1)

7^6 + 7^5 – 7^4 = 7^4(49 + 7 – 1)

7^6 + 7^5 – 7^4 = 7^4*55

7^6 + 7^5 – 7^4 = 7^4*5*11

7^6 + 7^5 – 7^4 = 11*5*7^4

7^6 + 7^5 – 7^4 = 11*k

Since the number is in the form 11*k, where k = 5*7^4, this proves that 7^6 + 7^5 – 7^4 is a multiple of 11.