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Speaker:

Alain S. Togbe
Affiliation:

Purdue University West Lafayette/MPIM
Date:

Wed, 14/06/2023 - 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar Let $k\geq 2$. A generalization of the well-known Pell sequence is the $k$-Pell sequence whose first $k$ terms are $0,\ldots,0,1$ and each term afterwards is given by the linear recurrence $$P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}.$$

The goal of this talk is to show that $11, 33, 55, 88$ and $99$ are only repdigits expressible as sum or difference of two $k$-Pell numbers. The proof of this main theorem uses lower bounds for linear forms in logarithms of algebraic numbers (Baker's method) and a modified version of Baker-Davenport reduction method (due to Dujella and Pethö). Our result extends that of Bravo and Herrera.

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