1. The problem is to rewrite the expression with the left side as $16|9(9^k+1-8k-17)$ and the rest divided by 16. 2. First, understand the notation: $16|9(9^k+1-8k-17)$ means $16 \times 9 \times (9^k + 1 - 8k - 17)$. 3. Simplify inside the parentheses: $$9^k + 1 - 8k - 17 = 9^k - 8k - 16$$ 4. Multiply by 9: $$9 \times (9^k - 8k - 16) = 9^{k+1} - 72k - 144$$ 5. Multiply by 16: $$16 \times (9^{k+1} - 72k - 144) = 16 \times 9^{k+1} - 1152k - 2304$$ 6. So the left side is: $$16 \times 9 \times (9^k + 1 - 8k - 17) = 16 \times 9^{k+1} - 1152k - 2304$$ 7. The rest of the expression should be divided by 16 as per your professor's instruction. Final expression: $$\frac{\text{rest}}{16}$$ where the left side is as above. This satisfies the requirement of having the left side as $16|9(9^k+1-8k-17)$ and the rest divided by 16.