S. S. Rout

activity

20132026

most citedOn the resolution of the Diophantine equation

U_{n} + U_{m} = x^{q}

2 citations · 5 across the 17 of their papers we have counts for

collaborators

17 papers

math.NT2026

Quantitative bounds on integrality for post-critically finite maps

Rudranarayan Padhy, Sudhansu Sekhar Rout

Let $K$ be a number field with algebraic closure $K$ and let $S$ be a finite set of places of $K$ that contain all the archimedean places. For an integer $d \geq 2$ , cons…

math.NT2025

On the number of irreducible representations of $\so(5)$

Saudamini Nayak, Nabin Kumar Meher, Sudhansu Sekhar Rout

Let $d (n)$ be the divisor function and it is well known that $\sum_{1 \leq n \leq x} d (n) = x lo g x + (2 γ - 1) x + O (x^{θ + ε})$ where $γ$ is the Euler constant, $ε > 0$ a…

math.NT2024

Zeros and $S$ -units in sums of terms of recurrence sequences in function fields

Darsana N, S. S. Rout

Let $(U_{n})_{n \geq 0}$ be a non-degenerate linear recurrence sequence with order at least two defined over a function field and $O_{S}^{*}$ be the set of $S$ -units. In this pa…

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…

math.NT2022★ 1 cited

On perfect powers that are sum of two balancing numbers

Pritam Kumar Bhoi, Sudhansu Sekhar Rout, Gopal Krishna Panda

Let $B_{k}$ denote the $k^{t h}$ term of balancing sequence. In this paper we find all positive integer solutions of the Diophantine equation $B_{n} + B_{m} = x^{q}$ in variables $(m, n, x, q)$ …

math.NT2022★ 2 cited

On the resolution of the Diophantine equation $U_{n} + U_{m} = x^{q}$

P. K. Bhoi, S. S. Rout, G. K. Panda

Suppose that $(U_{n})_{n \geq 0}$ is a binary recurrence sequence and has a dominant root $α$ with $α > 1$ and the discriminant $D$ is square-free. In this paper, we study the Diopha…

math.NT2021

Sums of $S$ -units in sum of terms of recurrence sequences

P. K. Bhoi, S. S. Rout, G. K. Panda

Let $S := {p_{1}, \dots, p_{ℓ}}$ be a finite set of primes and denote by $U_{S}$ the set of all rational integers whose prime factors are all in $S$ . Let $(U_n)_{n\geq 0…

math.NT2021

Reduction of polynomial dynamical systems modulo primes

Sudhansu Sekhar Rout

We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, usin…

math.NT2021

The orbit intersection problem in positive characteristic

Sudhansu Sekhar Rout

In this paper, we study the orbit intersection problem for the linear space and the algebraic group in positive characteristic. Let $K$ be an algebraically closed field of positive…

math.NT2020

Cullen numbers in sums of terms of recurrence sequence

Nabin Kumar Meher, Sudhansu Sekhar Rout

Let $(U_{n})_{n \geq 0}$ be a fixed linear recurrence sequence of integers with order at least two, and for any positive integer $ℓ$ , let $ℓ \cdot 2^{ℓ} + 1$ be a Cullen numb…

math.NT2020

$S$ -parts of sums of terms of linear recurrence sequences

S. S. Rout, N. K. Meher

Let $S = {p_{1}, \dots, p_{s}}$ be a finite, non-empty set of distinct prime numbers and $(U_{n})_{n \geq 0}$ be a linear recurrence sequence of integers of order $r$ . For any posit…

math.NT2020

Multiple Lucas Dirichlet series associated to additive and Dirichlet characters

Nabin Kumar Meher, Sudhansu Sekhar Rout

In this article, we obtain the analytic continuation of the multiple shifted Lucas zeta function, multiple Lucas $L$ -function associated to Dirichlet characters and additive charac…

math.NT2017

Perfect powers in alternating sum of consecutive cubes

Pranabesh Das, Pallab Kanti Dey, B. Maji +1

In this paper, we consider the problem about finding out perfect powers in an alternating sum of consecutive cubes. More precisely, we completely solve the Diophantine equation $(x…

math.NT2016

Linear combinations of prime powers in sums of terms of binary recurrence sequences

N. K. Meher, S. S. Rout

Let ${U_{n}}_{n \geq 0}$ be a non-degenerate binary recurrence sequence with positive discriminant. Let ${p_{1}, \dots, p_{s}}$ be fixed prime numbers and ${b_{1}, \dots, b_{s}}$ …

math.NT2016

Linear combinations of factorials in binary recurrence sequences

Sudhansu Sekhar Rout

Let ${u_{n}}_{n \geq 0}$ be a non-degenerate binary recurrence sequence with positive discriminant. In this paper, we consider the Diophantine equation $u_m + u_n = a_1 n_1! + \c…

math.NT2016★ 2 cited

Prime powers in sums of terms of binary recurrence sequences

Eshita Mazumdar, S. S. Rout

Let ${u_{n}}_{n \geq 0}$ be a non-degenerate binary recurrence sequence with positive, square-free discriminant and $p$ be a fixed prime number. In this paper, we have shown the…

math-ph2013

Affine Kac-Moody symmetric spaces associated with untwisted Kac-Moody algebras

Saudamini Nayak, S. S. Rout, K. C. Pati

In this paper we have computed all the affine Kac-Moody symmetric spaces which are tame Frechet manifolds starting from the Vogan diagrams related to the affine untwisted Kac-Moody…

Quantitative bounds on integrality for post-critically finite maps

On the number of irreducible representations of $\so(5)$

Zeros and S-units in sums of terms of recurrence sequences in function fields

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

On perfect powers that are sum of two balancing numbers

On the resolution of the Diophantine equation Un​+Um​=xq

Sums of S-units in sum of terms of recurrence sequences

Reduction of polynomial dynamical systems modulo primes

The orbit intersection problem in positive characteristic

Cullen numbers in sums of terms of recurrence sequence

S-parts of sums of terms of linear recurrence sequences

Multiple Lucas Dirichlet series associated to additive and Dirichlet characters

Perfect powers in alternating sum of consecutive cubes

Linear combinations of prime powers in sums of terms of binary recurrence sequences

Linear combinations of factorials in binary recurrence sequences

Prime powers in sums of terms of binary recurrence sequences

Affine Kac-Moody symmetric spaces associated with untwisted Kac-Moody algebras

Zeros and $S$ -units in sums of terms of recurrence sequences in function fields

On the resolution of the Diophantine equation $U_{n} + U_{m} = x^{q}$

Sums of $S$ -units in sum of terms of recurrence sequences

$S$ -parts of sums of terms of linear recurrence sequences