On Repdigits Which are Sums or Differences of Two k-Pell Numbers

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].