Parvathi S Nair

activity

20242026

collaborators

4 papers

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

The quotient problem for linear recurrence sequences

Parvathi S Nair, S. S. Rout

Let ${U (m)}_{m \in N}$ and ${V (n)}_{n \in N}$ be linear recurrence sequences. It is a well-known Diophantine problem to determine the finiteness of the set of natural numbers $…

math.NT2025

Algebraic approximations to linear combinations of S-units

Parvathi S Nair, Veekesh Kumar, S. S. Rout

Let $Γ\subset \bar{\Q}^{\times}$ be a finitely generated multiplicative group of algebraic numbers, let $α_{1}, \dots, α_{m}$ be non-zero algebraic numbers, and let $ε > 0$ be…

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…

Perfect powers with few digits and S-unit coefficients

The quotient problem for linear recurrence sequences

Algebraic approximations to linear combinations of S-units

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

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