B. Patel · wovepaper

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

collaborators

9 papers

On Diophantine equations involving intersection of Thabit and Williams numbers base $b$ and some ternary recurrent sequences

Bibhu Prasad Tripathy, Asutosh Satapathy, Utkal Keshari Dutta +1

Let $P_{n}$ be the $n$ -th Padovan number, $E_{n}$ be the $n$ -th Perrin number and $N_{n}$ be the $n$ -th Narayana's cows number. Let $b$ be a positive integer such that $b…

On balancing and Lucas-balancing numbers expressible as product of two $k$ -Fibonacci numbers

Bibhu Prasad Tripathy, Bijan Kumar Patel

A positive integer $n$ is called a balancing number if there exists a positive integer $r$ such that $1 + 2 + \dots + (n - 1) = (n + 1) + (n + 2) + \dots + (n + r)$ . The corresponding va…

Common terms of generalized Pell and Narayana's cows sequences

Bibhu Prasad Tripathy, Bijan Kumar Patel

For an integer $k \geq 2$ , let ${P_{n}^{(k)}}_{n}$ be the $k$ -generalized Pell sequence which starts with $0, \dots, 0, 1$ ( $k$ terms) and each term afterwards is the sum of $k$ p…

$k$ -Pell-Lucas numbers which are concatenations 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…

$k$ -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…

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…

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,…

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…