Bernadette Faye

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math.NT2026

On concatenations of two $k$ -generalized Pell numbers

Cherif B. Deme, Kancou D. Fall, Khady Faye +1

We study the concatenation of two $k$ -generalized Pell numbers. More precisely, we determine all solutions of the equation $P_{n}^{(k)} = P_{m}^{(k)} \cdot 1 0^{d} + P_{p}^{(k)}$ , where $…

math.NT2026

Multiplicative independence in the sequence of $k$ -generalized Pell numbers

Cherif B. Deme, Kancou D. Fall, Khady Faye +1

We study multiplicative dependence between terms of the $k$-generalized Pell sequence $(P_n^{(k)})_{n\ge 2-k}$, defined by the linear recurrence \[ P_n^{(k)}=2P_{n-1}^{(k)}+P_{…

math.NT2023

Pell and Pell-Lucas numbers as difference of two repdigits

Bilizimbeye Edjeou, Bernadette Faye

Let ${P_{n}}_{n \geq 0}$ be the sequence of Pell numbers defined by $P_{0} = 0$ , $P_{1} = 1$ and $P_{n + 2} = 2 P_{n + 1} + P_{n}$ for all $n \geq 0$ and let ${Q_{n}}_{n \geq 0}$ be its…

math.NT2023

Thue equations over $C (T)$ : The Complete Solution of a Simple quartic family

Bernadette Faye, Ingrid Vukusic, Ezra Waxman +1

In this paper we completely solve a simple quartic family of Thue equations over $C (T)$ . Specifically, we apply the ABC-Theorem to find all solutions $(x,y) \in \mathbb{C}…

On concatenations of two k-generalized Pell numbers

Multiplicative independence in the sequence of k-generalized Pell numbers

Pell and Pell-Lucas numbers as difference of two repdigits

Thue equations over C(T): The Complete Solution of a Simple quartic family

On concatenations of two $k$ -generalized Pell numbers

Multiplicative independence in the sequence of $k$ -generalized Pell numbers

Thue equations over $C (T)$ : The Complete Solution of a Simple quartic family