Divyum Sharma

most citedOn the representation of an imaginary quadratic integer in two different bases

1 citations · 1 across the 2 of their papers we have counts for

collaborators

2 papers

math.NT2025

Representing an integer and its powers in two unrelated number systems

Divyum Sharma, L. Singhal

Let $α$ be a fixed quadratic irrational. Consider the Diophantine equation \[ y^a\ =\ q_{N_1} + \cdots + q_{N_K},\quad N_1 \geq \cdots \geq N_{K} \geq 0,\quad a, y \geq 2 \] where…

math.NT2023★ 1 cited

On the representation of an imaginary quadratic integer in two different bases

Divyum Sharma

Let $(α, N_{α})$ and $(β, N_{β})$ be two canonical number systems for an imaginary quadratic number field $K$ such that $α$ and $β$ are multiplicatively independent.…