# Where do I start?

## Main Question or Discussion Point

Can someone point me in the right direction of solving the following problem:

Prove that for any postive integer n, the value of the expression $$3^{2n+2} - 8n -9$$ is divisible by 64.

Last edited:

honestrosewater
Gold Member
I find when you're asked to prove that every member of some subset of the natural numbers has some property, induction usually works.

matt grime
Homework Helper
9^{n+1}-8n-9

or equivalently

9^n-8n-1

what is the binomial expansion of 9^n when considering 9=8+1?

honestrosewater
Gold Member
Maybe I'm having a blonde moment, but doesn't $a^{n + 1} - a = a(a^{n} - 1)$, making $9^{n + 1} - 9 - 8n = 9(9^{n} - 1) - 8n$?

matt grime