Bunyakovsky conjecture for cyclotomic polynomials

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This article on Wikipedia: http://en.wikipedia.org/wiki/Bunyakovsky_conjecture says:

In fact, it can be shown that if for all natural number $ n $, there exists a natural number $ x > 1 $ such that $ \Phi_n(x) $ is prime, then for all natural number $ n $, there are infinitely many natural number $ x $ such that $ \Phi_n(x) $ is prime.

(Where $ \Phi_n(x) $ is the $ n $-th cyclotomic polynomial)

However, there is no reference to the proof. Could you please post the proof or a link to it?

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I'm not sure where this claim originally came from or what the intended proof of it was, but it follows quite easily from one property of cyclotomic polynomials (Wikipedia link): $$\Phi_n(x) = \Phi_q(x^{n/q}),$$ where $q$ is the largest square-free factor of $n$. From this property, we see that if $p$ is a prime dividing $n$, then, since the largest square-free divisor of $p^k n$ is also $q$, $$\Phi_{p^k n}(x) = \Phi_q(x^{p^k n/q}) = \Phi_q((x^{p^k})^{n/q}) = \Phi_n(x^{p^k}).$$ Suppose that, for all $n$, we can find an integer $x>1$ such that $\Phi_n(x)$ is prime. Then, in particular, we can find integers $x_1, x_2, \dots$ such that $\Phi_{p^k n}(x_k)$ is prime, for each $k$. But this means that $\Phi_n((x_k)^{p^k})$ is prime, for each $k$. So the sequence $$(x_1)^p, (x_2)^{p^2}, (x_3)^{p^3}, \dots$$ is an infinite sequence of values at which $\Phi_n$ is prime. (Some of these values might happen to repeat, but that's okay, since each value can only repeat finitely many times.)