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- Title
On Repdigits Which are Sums or Differences of Two k-Pell Numbers.
- Authors
Faye, Mariama Ndao; Rihane, Salah Eddine; Togbé, Alain
- Abstract
Let k ≥ 2. A generalization of the well-known Pell sequence is the k-Pell sequence whose first k terms are 0,..., 0, 1 and each term afterwards is given by the linear recurrence p n (k) = 2 P n − 1 (k) + P n − 2 (k) + ⋯ + P n − k (k) . The goal of this paper is to show that 11, 33, 55, 88 and 99 are all repdigits expressible as sum or difference of two k-Pell. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a modified version of Baker-Davenport reduction method (due to Dujella and Pethő). This extends a result of Bravo and Herrera [Repdigits in generalized Pell sequences, Arch. Math. (Brno) 56(4) (2020), 249–262].
- Subjects
ALGEBRAIC numbers; MONOPULSE radar; LOGARITHMS; SHIFT registers; MATHEMATICS; GENERALIZATION
- Publication
Mathematica Slovaca, 2023, Vol 73, Issue 6, p1409
- ISSN
0139-9918
- Publication type
Article
- DOI
10.1515/ms-2023-0102