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PreprintCC BY 4.0arXiv

The local Dold congruence for Fibonacci and Lucas sequences

  • Sompong Chuysurichay
  • Sawian Jaidee
  • Chatchawan Panraksa
  • Thomas Ward
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Abstract

We discuss local properties of the classical Fibonacci and Lucas sequences, characterising in both cases those primes~p for which the~p-part satisfies the Dold congruences or is realizable. We calculate an exact `repair' multiplier in each case and determine the relative prime densities of the Dold, realizable, almost Dold, and almost realizable prime sets. In that order, the four densities are~(3/4,1/3,1,1/3) for the Lucas sequence and~(1/2,1/2,1,1) for the Fibonacci sequence.

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Cite

BibTeXRIS
BibTeX
@misc{chuysurichay2026local,
  title = {{The local Dold congruence for Fibonacci and Lucas sequences}},
  author = {Sompong Chuysurichay and Sawian Jaidee and Chatchawan Panraksa and Thomas Ward},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24544},
  eprint = {2609.24544},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24544},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The local Dold congruence for Fibonacci and Lucas sequences
AU  - Sompong Chuysurichay
AU  - Sawian Jaidee
AU  - Chatchawan Panraksa
AU  - Thomas Ward
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24544
UR  - https://arxiv.org/abs/2609.24544
AB  - We discuss local properties of the classical Fibonacci and Lucas sequences, characterising in both cases those primes~p for which the~p-part satisfies the Dold congruences or is realizable. We calculate an exact `repair' multiplier in each case and determine the relative prime densities of the Dold, realizable, almost Dold, and almost realizable prime sets. In that order, the four densities are~(3/4,1/3,1,1/3) for the Lucas sequence and~(1/2,1/2,1,1) for the Fibonacci sequence.
ER  -