Primitive Divisors of some Lehmer-Pierce Sequences

Abstract

We study the primitive divisors of the terms of $({\Delta }_n{)}_{n\ge 1}$, where ${\Delta }_n=N_{K/\mathbb{Q}}(u^n-1)$ for $K$ a real quadratic field, and $u>1$ 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.

10 pages