D. Behloul

collaborators

2 papers

math.NT2023

$k$ -Fibonacci numbers which are Narayana's cows numbers

Hayat Bensella, Djilali Behloul

In this paper,we find all generalized Fibonacci numbers which are Narayana's cows numbers. In our proofs, we use both Baker's theory of nonzero linear forms in logarithms of algebr…

math.NT2022

On the Exponential Diophantine Equation $(F_{m + 1}^{(k)})^{x} - (F_{m - 1}^{(k)})^{x} = F_{n}^{(k)}$

Hayat Bensella, Bijan Kumar Patel, Djilali Behloul

In this paper, we explicitly find all solutions of the title Diophantine equation, using lower bounds for linear forms in logarithms and properties of continued fractions. Further,…

k-Fibonacci numbers which are Narayana's cows numbers

On the Exponential Diophantine Equation (Fm+1(k)​)x−(Fm−1(k)​)x=Fn(k)​

$k$ -Fibonacci numbers which are Narayana's cows numbers

On the Exponential Diophantine Equation $(F_{m + 1}^{(k)})^{x} - (F_{m - 1}^{(k)})^{x} = F_{n}^{(k)}$