Primitive divisors of some Lehmer–Pierce sequences

We study primitive prime divisors of the terms of Δ(u)=(Δn(u))n⩾1, where Δn(u)=NK/Q(un−1) for K a real quadratic field, and u a unit element of its ring of integers. The methods used allow us to find the terms of the sequence that do not have a primitive prime divisor.