Primitive Divisors of some Lehmer-Pierce Sequences

2007/08/16 by Anthony Flatters, Flatters, Anthony
Mathematics · #11A51 #11B37 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A51 #msc:11B37

paper · pdf · doi:10.48550/arxiv.0708.2190

10 pages

arxiv created 2007/08/16 · arxiv updated 2009/12/01

Abstract

We study the primitive divisors of the terms of (Δ_n)_{n ≥ 1}, where Δ_n=N_{K/ ℚ}(uⁿ-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.

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