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On Repdigits Which are Sums or Differences of Two k-Pell Numbers.
- Source :
- Mathematica Slovaca; Dec2023, Vol. 73 Issue 6, p1409-1422, 14p
- Publication Year :
- 2023
-
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]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01399918
- Volume :
- 73
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Mathematica Slovaca
- Publication Type :
- Academic Journal
- Accession number :
- 174295740
- Full Text :
- https://doi.org/10.1515/ms-2023-0102