S. Rout

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20242026

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math.NT2026

Perfect powers with few digits and $S$ -unit coefficients

Darsana N, Parvathi S Nair, Sudhansu Sekhar Rout

In this paper, we study two questions concerning perfect powers in $S$ -unit equations and sparse representations of perfect powers. Corvaja-Zannier \cite{corvaja2013finiteness} pro…

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 $(U_{n} (ζ))_{n \geq 0}$ . 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…

Perfect powers with few digits and S-unit coefficients

Prime ideal divisors of parametric recurrence sequences

Uniform bounds on S-integral points in backward orbits

Perfect powers with few digits and $S$ -unit coefficients

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