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Math Help - Induction Proof

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    Exclamation Induction Proof

    Prove the following: 9^n - 8n + 63 is a multiple of 64 for all n that are elements of N(natural numbers). I'm having a hard time pulling out the coefficients to get a multiple. thanks in advance!
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    Quote Originally Posted by Kinetix View Post
    Prove the following: 9^n - 8n + 63 is a multiple of 64 for all n that are elements of N(natural numbers). I'm having a hard time pulling out the coefficients to get a multiple. thanks in advance!
    Skipping to step 3:

    You need to show that 9^{k+1} - 8(k+1) + 63 is a multiple of 64 under the assumption that 9^k - 8k + 63 is a multiple of 64.

    Note:

    9^{k+1} - 8(k+1) + 63 = 9 (9^k) - 8k + 55

    = 9 (9^k - 8k + 63) + 64k - 504 = 9 (9^k - 8k + 63) + 64(k - 8).
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