1. ## 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!

2. Originally Posted by Kinetix
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:

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

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