I have recently happened upon an interesting problem that I cannot solve. Here it is:

a. Factorise $\displaystyle x^3+1$.

b. Factorise $\displaystyle x^n+1$ when $\displaystyle {n}\geq{3}$ is odd. Use this to prove the following:

i. If $\displaystyle 2^n+1$ is prime, then $\displaystyle n$ must be a power of $\displaystyle 2$.

ii. Show that $\displaystyle 2^3^2+1$ isnotprime.

I can't seem to make any headway on the problem, in particular the very last part. All help is appreciated on this problem.