Question

Show that $9^{n+1}-8n-9$ is divisible by $64$, whenever n is a positive integer.

Answer 1

Numbers divisible by $64$ are

$64=64\times 1$

$128=64\times 2$

$640=64\times 10$

Any number divisible by $64=64\times$ Natural number

Hence, In order to show that ${}^{9}n+1-8n-9$ is divisible by $64$,

We have to prove that

$9^{n+1}-8n-9=64k$, where $k$ is some natural number