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arXiv · 2609.05693

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

Kouèssi Norbert Adédji·Marija Bliznac Trebješanin·Jelena Pleština
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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.

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Kouèssi Norbert Adédji, Marija Bliznac Trebješanin, Jelena Pleština. 2026-09-04. On the Diophantine Equations Arising from Three-Term $b$-Concatenations in Pell-Type Sequences. https://arxiv.org/abs/2609.05693

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