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

Question

Macie Cortez

Mathematics

20 December, 19:43

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

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Answers (1)

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Cecelia Frost · Answer 1

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.