Divyum Sharma

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20242026

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math.NT2026

Additive Diophantine Equations involving S-Units, Factorials and Ternary Recurrences with repeated root

Vikas Godara, Divyum Sharma

Let $C_{n} = n 2^{n} + 1$ denote the $n$ th Cullen number. There has been recent interest in finding all Cullen numbers having a given Diophantine property. We prove that, for a fixed intege…

math.NT2025

Explicit and Mixed Estimates for Thue inequalities with few coefficients

N. Saradha, Divyum Sharma

Let $F (x, y)$ be an irreducible form of degree $r \geq 3$ and having $s + 1$ non-zero coefficients. Let $h \geq 1$ be an integer and consider the Thue inequality $∣ F (x, y) ∣ \leq h .$ Fol…

math.NT2024

On the representation of an integer in Ostrowski and recurrence numeration systems

Mohit Mittal, Divyum Sharma

We provide an effective upper bound for positive integers with bounded Hamming weights with respect to both a linear recurrence numeration system and an Ostrowski- $I^\pm$ numeration s…