I recently happened upon a problem that I cannot make any headway on. Here it is:

Using the factorization of $\displaystyle x^n+1$ when $\displaystyle n\geq 3$ and is odd, show that $\displaystyle 2^3^2+1$ is not prime.

I found this video, YouTube - the 5th Fermat number is not a prime (german), that shows this, but, unfortunately, I don't think that it uses the factorization of $\displaystyle x^n+1$ when $\displaystyle n\geq 3$ and is odd and I don't know how to adapt it so that it does (if that is possible at all).

Thank you. All help with this problem is appreciated.