S. Rout

activity

20242026

collaborators

6 papers

math.NT2026

Prime ideal divisors of parametric recurrence sequences

Darsana N, Sudhansu Sekhar Rout

We prove new arithmetic results for parametric linear recurrence sequences specialized at roots of unity, denoted by $(U_{n} (I^¶))_{n \geq 0}$ . In particular, we obtain effective lower…

math.NT2026

Uniform bounds on $S$ -integral points in backward orbits

R. Padhy, S. S. Rout

Let $K$ be a number field with algebraic closure $K$ and let $S$ be a finite set of places of $K$ containing all the archimedean places. It is known from Silverman's res…

math.NT2025

Diophantine Equations for Polynomial Recursive Sequences

Darsana N, Sudhansu Sekhar Rout

We study the Diophantine equation of type $U_{n} (x) = V_{m} (y)$ , where $(U_{n})_{n \geq 0}$ and $(V_{m})_{m \geq 0}$ are polynomial power sums defined over a number field $K$ . By applying the…

math.NT2025

Primitive prime divisors in the forward orbit of a polynomial

Shanta Laishram, Sudhansu S. Rout, Prabhakar Yadav

For the polynomial $f (z) \in Q [z]$ , we consider the Zsigmondy set $Z (f, 0)$ associated to the numerators of the sequence ${f^{n} (0)}_{n \geq 0}$ . In this paper, w…

math.NT2024

Sums of S-units in X-coordinates of Pell equations

Parvathi S Nair, Sudhansu Sekhar Rout

Let $S$ be a fixed set of primes and let $(X_{l})_{l \geq 1}$ be the $X$ -coordinates of the positive integer solutions $(X, Y)$ of the Pell equation $X^{2} - d Y^{2} = 1$ corresponding to…

math.NT2024

Uniform bounds on $S$ -integral preperiodic points for chebyshev polynomials

Rudranarayan Padhy, Sudhansu Sekhar Rout

Let $K$ be a number field with algebraic closure $K ˉ$ , let $S$ be a finite set of places of $K$ containing the archimedean places, and let $I ¨ $ be Chebyshev polynomial. In thi…