P. K. Bhoi

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20242026

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math.NT2026

Resolution of the Skolem Problem for $k$ -Generalized Lucas Sequences

Monalisa Mohapatra, Pritam Kumar Bhoi, Gopal Krishna Panda

This paper provides a complete solution to Skolem's problem for the $k$ -generalized Lucas sequence $(L_{n}^{(k)})_{n \in Z}$ with a primary focus on its behavior at negative…

math.NT2025

Solving Skolem problem for negative indexed $k -$ generalized Pell numbers

Monalisa Mohapatra, Pritam Kumar Bhoi, Gopal Krishna Panda

In this paper, we address the Skolem problem for the $k$ -generalized Pell sequence $(P_{n}^{(k)})_{n \geq 2 - k}$ extended to negative indices. We focus on identifying and bounding the i…

math.NT2024

Balancing and Lucas-balancing numbers as difference of two repdigits

Monalisa Mohapatra, Pritam Kumar Bhoi, Gopal Krishna Panda

Positive integers with all digits equal are called repdigits. In this paper, we find all balancing and Lucas-balancing numbers, which can be expressed as the difference of two repd…

math.NT2024

Sum of terms of recurrence sequences in the solution sets of generalized Pell equations

Pritam Kumar Bhoi, Rudranarayan Padhy, Sudhansu Sekhar Rout

Let $(X_{k})_{k \geq 1}$ and $(Y_{k})_{k \geq 1}$ be the sequence of $X$ and $Y$ -coordinates of the positive integer solutions $(x, y)$ of the equation $x^{2} - d y^{2} = t$ . In this paper…

Resolution of the Skolem Problem for k-Generalized Lucas Sequences

Solving Skolem problem for negative indexed k−generalized Pell numbers

Balancing and Lucas-balancing numbers as difference of two repdigits

Sum of terms of recurrence sequences in the solution sets of generalized Pell equations

Resolution of the Skolem Problem for $k$ -Generalized Lucas Sequences

Solving Skolem problem for negative indexed $k -$ generalized Pell numbers