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9 April, 02:10

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

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  1. 9 April, 02:16
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    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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