(In reply to solution
Excellent expose, Paul.
I would like to post it as an "official" solution, - with a small modification- after the case of n=1 the sequel will be as follows:
...Let us consider n>1.
Clearly, when n is odd - x^n + 1 is even, and therefore not prime.
Now for odd values of n etc etc
I hope to get your approval of the above clarification.