Bernadette Faye

collaborators

3 papers

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

On a simple quartic family of Thue equations over imaginary quadratic number fields

Benjamin Earp-Lynch, Bernadette Faye, Eva G. Goedhart +2

Let $t$ be any imaginary quadratic integer with $∣ t ∣ \geq 100$ . We prove that the inequality \[ |F_t(X,Y)| = | X^4 - t X^3 Y - 6 X^2 Y^2 + t X Y^3 + Y^4 | \leq 1 \] has only trivial…

math.NT2016

Power of Two as sums of Three Pell Numbers

Jhon J. Bravo, Bernadette Faye, Florian Luca

In this paper, we find all the solutions of the Diophantine equation $P_{ℓ} + P_{m} + P_{n} = 2^{a}$ , in nonnegative integer variables $(n, m, ℓ, a)$ where $P_{k}$ is the $k$ -th term of the…