Arkabrata Ghosh

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

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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…

Solution of the Diophantine equation x2+pk=yn

General Solution of the Diophantine equation involving Mersenne Prime

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