Bernadette Faye

activity

20152023

collaborators

11 papers

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.NT2019

Separating singular moduli and the primitive element problem

Yuri Bilu, Bernadette Faye, Huilin Zhu

We prove that $∣ x - y ∣ \geq 800 X^{- 4}$ , where $x$ and $y$ are distinct singular moduli of discriminants not exceeding $X$ . We apply this result to the "primitive element problem" for t…

math.NT2018

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Salah E. Rihane, Bernadette Faye, Florian Luca +1

In this paper, we find all solutions of the exponential Diophantine equation $B_{n + 1}^{x} - B_{n}^{x} = B_{m}$ in positive integer variables $(m, n, x)$ , where $B_{k}$ is the $k$ -th term of the…

math.NT2018

Fields generated by sums and products of singular moduli

Bernadette Faye, Antonin Riffaut

We show that the field $Q (x, y)$ , generated by two singular moduli~ $x$ and~ $y$ , is generated by their sum $x + y$ , unless~ $x$ and~ $y$ are conjugate over~ $Q$ , in wh…

math.NT2017

Diophantine Equation with Arithmetic functions and Binary recurrent sequences

Bernadette Faye

This thesis is about the study of Diophantine equations involving binary recurrent sequences with arithmetic functions. Various Diophantine problems are investigated and new result…

math.NT2017

On the discriminator of Lucas sequences

Bernadette Faye, Florian Luca, Pieter Moree

We consider the family of Lucas sequences uniquely determined by $U_{n + 2} (k) = (4 k + 2) U_{n + 1} (k) - U_{n} (k),$ with initial values $U_{0} (k) = 0$ and $U_{1} (k) = 1$ and $k \geq 1$ an arbitrary inte…

cs.CR2017

Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus $2$

Bernadette Faye

Here, we proposed an improved version of the deterministic random extractors $S E J$ and $P E J$ proposed by R. R. Farashahi in \cite{F} in 2009. By using the Mumford's representation…

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…

math.NT2015

Pell Numbers with Lehmer property

Bernadette Faye, Florian Luca

In this paper, we prove that there is no number with the Lehmer property in the sequence of Pell numbers.

math.NT2015

Pell Numbers whose Euler Function is a Pell Number

Bernadette Faye, Florian Luca

In this paper, we show that the only Pell numbers whose Euler function is also a Pell number are $1$ and $2$ .

math.NT2015

Lucas Numbers with Lehmer Property

Bernadette Faye, Florian Luca

A composite positive integer n is Lehmer if ϕ(n) divides n-1, where ϕ(n) is the Euler's totient function. No Lehmer number is known, nor has it been proved that they don't exist. I…

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

Separating singular moduli and the primitive element problem

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Fields generated by sums and products of singular moduli

Diophantine Equation with Arithmetic functions and Binary recurrent sequences

On the discriminator of Lucas sequences

Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus 2

Power of Two as sums of Three Pell Numbers

Pell Numbers with Lehmer property

Pell Numbers whose Euler Function is a Pell Number

Lucas Numbers with Lehmer Property

Extracting a uniform random bit-string over Jacobian of Hyperelliptic curves of Genus $2$