B. Patel

activity

20202025

most citedPell and Pell-Lucas numbers as sums of three repdigits

2 citations · 2 across the 7 of their papers we have counts for

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math.NT2022

$k$ -Pell-Lucas numbers as Product of Two Repdigits

Bibhu Prasad Tripathy, Bijan Kumar Patel

For any integer $k \geq 2$ , let ${Q_{n}^{(k)}}_{n \geq - (k - 2)}$ denote the $k$ -generalized Pell-Lucas sequence which starts with $0, \dots, 2, 2$ ( $k$ terms) where each next term…

math.NT2022

Sums of three Fibonacci numbers close to a power of 2

Bibhu Prasad Tripathy, Bijan Kumar Patel

In this paper, we find all the sums of three Fibonacci numbers which are close to a power of 2. This paper continues and extends the previous work of Hasanalizade \cite{Hasanalizad…

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-Pell-Lucas numbers as Product of Two Repdigits

Sums of three Fibonacci numbers close to a power of 2

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

$k$ -Pell-Lucas numbers as Product of Two Repdigits

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