Bernadette Faye

collaborators

6 papers

math.NT2026

Pillai's equation between k-generalized Pell numbers and Tribonacci numbers

Cherif B. Deme, Kancou D. Fall, Bernadette Faye

For an integer $k \geq 2$ , let $(P_{n}^{(k)})_{n \geq 0}$ be the $k$ -generalized Pell sequence and $(T_{m})_{m \geq 1}$ the Tribonacci sequence. We determine, for every $k \geq 2$ , all integers $c…

math.NT2026

Tribonacci numbers that are palindromic concatenations of two distinct repdigits

Khady Faye, Bernadette Faye

Let $(T_{n})_{n \geq 1}$ be the Tribonacci sequence, defined by $T_{1} = T_{2} = 1$ , $T_{3} = 2$ , and $T_{n} = T_{n - 1} + T_{n - 2} + T_{n - 3}$ for $n \geq 4$ . In this paper, we study the Tribonacci numbers whose…

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}…

Pillai's equation between k-generalized Pell numbers and Tribonacci numbers

Tribonacci numbers that are palindromic concatenations of two distinct repdigits

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