Arkabrata Ghosh

most citedThe Prym variety of a dilated double cover of metric graphs

1 citations · 1 across the 4 of their papers we have counts for

collaborators

4 papers

math.NT2024

A necessary condition for $2 p$ to be congruent for a prime $p \equiv 5 (mod 8)$

Arkabrata Ghosh

In this article, we consider primes $p \equiv 5 (mod 8)$ and are able to prove that $p \equiv 5 (mod 16)$ if $2 p$ is a congruent number.

math.NT2024

Solution of the Diophantine equation $x^{2} + p^{k} = y^{n}$

Arkabrata Ghosh

The main aim of this article is to find all solutions of the Diophantine equation $x^{2} + p^{k} = y^{n}$ where $p \equiv 1 (mod 4)$ , $\frac{p - 1}{3}$ is a perfect square and the class numb…

math.NT2023

General Solution of the Diophantine equation involving Mersenne Prime

Arkabrata Ghosh

In this article, I study and solve the exponential Diophantine equation $M_{p}^{x} + (M_{q} + 1)^{y} = (l z)^{2}$ where $M_{p}$ and $M_{q}$ are Mersenne primes, $l$ is a prime number, and $x,y…

math.CO2023★ 1 cited

The Prym variety of a dilated double cover of metric graphs

Arkabrata Ghosh, Dmitry Zakharov

We calculate the volume of the tropical Prym variety of a harmonic double cover of metric graphs having non-trivial dilation. We show that the tropical Prym variety behaves discont…

A necessary condition for 2p to be congruent for a prime p≡5(mod8)

Solution of the Diophantine equation x2+pk=yn

General Solution of the Diophantine equation involving Mersenne Prime

The Prym variety of a dilated double cover of metric graphs

A necessary condition for $2 p$ to be congruent for a prime $p \equiv 5 (mod 8)$

Solution of the Diophantine equation $x^{2} + p^{k} = y^{n}$