PreprintCC BY-NC-ND 4.0arXiv
On the Diophantine Equations Arising from Three-Term b-Concatenations in Pell-Type Sequences
Abstract
We study the Diophantine problem of representing a Pell or Pell--Lucas number as the base-b concatenation of three other Pell or Pell--Lucas numbers. Under the condition that the index of the middle block does not exceed that of the leading block, we obtain an explicit upper bound for the sequence indices in terms of b. For 2≤ b≤15, we determine exactly $51$ solutions up to the identification Q0=Q1=2, while there are $74$ solutions when distinct index choices are counted separately.
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BibTeX
@misc{adedji2026diophantine,
title = {{On the Diophantine Equations Arising from Three-Term $b$-Concatenations in Pell-Type Sequences}},
author = {Kouèssi Norbert Adédji and Marija Bliznac Trebješanin and Jelena Pleština},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05693},
eprint = {2609.05693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05693},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On the Diophantine Equations Arising from Three-Term b-Concatenations in Pell-Type Sequences
AU - Kouèssi Norbert Adédji
AU - Marija Bliznac Trebješanin
AU - Jelena Pleština
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05693
UR - https://arxiv.org/abs/2609.05693
AB - We study the Diophantine problem of representing a Pell or Pell--Lucas number as the base-b concatenation of three other Pell or Pell--Lucas numbers. Under the condition that the index of the middle block does not exceed that of the leading block, we obtain an explicit upper bound for the sequence indices in terms of b. For 2≤ b≤15, we determine exactly $51$ solutions up to the identification Q_0=Q_1=2, while there are $74$ solutions when distinct index choices are counted separately.
ER -