Jacobsthal and Jacobsthal-Lucas numbers with Lehmar property
Ala'a Al-Kateeb
TL;DR
This paper proves that Jacobsthal and Jacobsthal-Lucas sequences do not contain any numbers with the Lehmer property, clarifying a specific number-theoretic characteristic of these sequences.
Contribution
It establishes the non-existence of Lehmer numbers within Jacobsthal and Jacobsthal-Lucas sequences, a novel result in the study of these sequences.
Findings
No Jacobsthal numbers have the Lehmer property.
No Jacobsthal-Lucas numbers have the Lehmer property.
The sequences lack numbers with this specific number-theoretic property.
Abstract
In this note, we prove that there is no number with the Lehmer property in the sequences of Jaconsthsl or Jacobsthal-Lucas numbers.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Mathematics and Applications · Mathematical Dynamics and Fractals