A property of primitive prime divisors of \(\Phi_ d (a)\) (Q1345828)

Let \(d\geq 1\) and \(a\geq 2\). The author characterizes the numbers \(n\in \mathbb{N}\) which divide \(\Phi_d (a^n)\), where \(\Phi_d\) denotes a cyclotomic polynomial. If \((a, d)\neq (2,1)\), then there exist infinitely many \(n\) with this property.