**Solution:
**

n = 1 ⇒ 9^{n + 1} - 8n - 9 = 9^{2} - 8 - 9

= 81 - 17 = 64= 1 x (64)

n = 2 ⇒9^{n + 1} - 8n - 9 = 9^{3} - 8(2) - 9

= 729 – 16 - 9 = 704= 11 x (64)

From n = 3, 4, 5,.....9^{n + 1} – 8n - 9 = 9^{(1 + 8)n} - 8n - 9

= 9 [nC0 + nC1 . 8 + nC2.8^{2} + ... nCn x 8^{n}] – 8n - 9

= 9[1 + 8n + nC2.8^{2} + ... nCn x 8^{n}] –8n – 9

= 9 + 72n + 9. nC2. 8^{2} + ... 9 x nCn x 8^{n} –8n - 9

= 8^{2} [n + 9 (nC2 + nC3.8 +... nCn 8^{n-2})]

which is divisible by 64.