2025/107/3-4 (11)
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DOI: 10.5486/PMD.2025.10230
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pp. 477-498
On the Lucas and Lehmer sequences in Dedekind domains
Authors:
Xiumei Li 
, Giulio Peruginelli and Min Sha
Abstract:
In this paper, we first obtain the strong divisibility property for the Lucas and Lehmer sequences in Dedekind domains, and then establish analogues of Zsigmondy's theorem and the primitive divisor results for such sequences in function fields.
Keywords: primitive divisor, Zsigmondy's theorem, Lucas sequence, Lehmer sequence, Dedekind domain, function field
Mathematics Subject Classification: 11A41, 11B39, 13F05