Work

On the Diophantine Equations Arising from Three-Term $b$-Concatenations in Pell-Type Sequences

Year: 2026

Type: preprint

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 $2\leq b\leq15$, 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.05693

Authors: Adédji, Kouèssi Norbert, Trebješanin, Marija Bliznac, Pleština, Jelena

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Ulsan National Institute of Science and Technology

OpenAlex ID: W7211985793

Cites: 8

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Related to: 10