Prove that $n^{34}-9$ is never prime for any $n$.

Question

It is given in the book 'Introduction to Number Theory' by 'William W. Adams, Larry Joel Goldstein' as Q. 17 in sec. 2.4 (titled: Unique Factorization) exercise:

Prove that $n^{34}-9$ is never prime for any $n$.

If $n$ is prime, then any power of it wouldn't be a prime. But, what is the significance of subtracting $9$ from $n^{34}$ is not clear.

Answer 1

Hint. $a^2-b^2=(a+b)(a-b)$ is never prime for integers $a,b$, unless either $a+b$ or $a-b$ is $\pm 1$.

Answer 2

$(n^{34} - 9)$ can be express as $(n^{17}-3)(n^{17}+3)$ so it is not prime $\forall n$