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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]

Let k ≥ 2 . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence the 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). In this manuscript, our main objective is to find all k-Pell numbers which are product of two repdigits. This generalizes a result of Erduvan and Keskin (Pell and Pell–Lucas numbers as products of two repdigits, submitted) regarding Pell numbers with the above property. [ABSTRACT FROM AUTHOR]