Divyum Sharma

activity

20162026

most citedOn the coefficient-choosing game

1 citations · 1 across the 9 of their papers we have counts for

collaborators

9 papers

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- $α$ numeration sy…

math.NT2022

Diagonalizable Thue Equations -- revisited

N. Saradha, Divyum Sharma

Let $r, h \in N$ with $r \geq 7$ and let $F (x, y) \in Z [x, y]$ be a binary form such that \[ F(x , y) =(αx + βy)^r -(γx + δy)^r, \] where $α$ , $β$ , $γ$ and $δ$ are alge…

math.NT2021

Rational solutions to the Variants of Erdős- Selfridge superelliptic curves

Pranabesh Das, Shanta Laishram, N. Saradha +1

For the superelliptic curves of the form $(x + 1) \dots (x + i - 1) (x + i + 1) \dots (x + k) = y^{ℓ}$ with $x, y \in Q$ , $y \neq = 0$ , $k \geq 3$ , $1 \leq i \leq k$ , $ℓ \geq 2,$ a prim…

math.NT2020★ 1 cited

On the coefficient-choosing game

Divyum Sharma, L. Singhal

Nora and Wanda are two players who choose coefficients of a degree $d$ polynomial from some fixed unital commutative ring $R$ . Wanda is declared the winner if the polynomial has a…

math.NT2017

Joint distribution in residue classes of the base- $q$ and Ostrowski digital sums

Divyum Sharma

Let $q$ be an integer $\geq 2$ and let $S_{q} (n)$ denote the sum of digits of $n$ in base $q$ . For \[ α=[0;\overline{1,m}],\ m\geq 2, \] let $S_{α} (n)$ denote the sum of digits in the…

math.NT2016

Contributions to a conjecture of Mueller and Schmidt on Thue inequalities

N. Saradha, Divyum Sharma

Let $F (X, Y) = i = 0 \sum s a_{i} X^{r_{i}} Y^{r - r_{i}} \in Z [X, Y]$ be a form of degree $r = r_{s} \geq 3$ , irreducible over $Q$ and having at most $s + 1$ non-zero coefficient…

math.NT2016

Thue's inequalities and the hypergeometric method

Shabnam Akhtari, N. Saradha, Divyum Sharma

Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape $0 < ∣ F (x, y) ∣ \leq h$ , where $F(x ,…

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

Explicit and Mixed Estimates for Thue inequalities with few coefficients

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

Diagonalizable Thue Equations -- revisited

Rational solutions to the Variants of Erdős- Selfridge superelliptic curves

On the coefficient-choosing game

Joint distribution in residue classes of the base-q and Ostrowski digital sums

Contributions to a conjecture of Mueller and Schmidt on Thue inequalities

Thue's inequalities and the hypergeometric method

Joint distribution in residue classes of the base- $q$ and Ostrowski digital sums