B. Patel

activity

20202022

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

2 citations · 2 across the 3 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

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,…

math.NT2021

Diophantine Equation with Balancing-like Sequences Associated to the Pillai-Tijdeman-type Problem

Bijan Kumar Patel, Prashant Tiwari

Let ${x_{n}}_{n \geq 0}$ be the balancing-like sequence defined by $x_{n + 1} = A x_{n} - x_{n - 1}$ , for $A > 2$ , where $x_{0} = 0$ and $x_{1} = 1$ . In this paper, we demonstrate how to f…

math.NT2020★ 2 cited

Pell and Pell-Lucas numbers as sums of three repdigits

Kisan Bhoi, Bijan Kumar Patel, Prasanta Kumar Ray

In this study, we find all Pell and Pell-Lucas numbers which are sums of three base 10 repdigits. The proof of our main theorem uses lower bounds for linear forms in logarithms of…

k-Pell-Lucas numbers as Product of Two Repdigits

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

Diophantine Equation with Balancing-like Sequences Associated to the Pillai-Tijdeman-type Problem

Pell and Pell-Lucas numbers as sums of three repdigits

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

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