Primitive divisors of some Lehmer–Pierce sequences

Abstract

We study primitive prime divisors of the terms of Δ ( u ) = ( Δ n ( u ) ) n ⩾ 1 , where Δ n ( u ) = N K / Q ( u n − 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.