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

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

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3 months 2022-02-15T10:18:44+00:00 1 Answer 0 views 0

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    2022-02-15T10:19:51+00:00

    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.

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45:7+7-4:2-5:5*4+35:2 =? ( )