P. Das

activity

20142026

most citedInvitation to Integral and Rational points on curves and surfaces

5 citations · 8 across the 4 of their papers we have counts for

collaborators

6 papers

math.NT2026

Improved exponent bounds for Erdős--Selfridge curves

Pranabesh Das, Kyle Pratt

Given integers $k, ℓ \geq 2$ , define the Erdős--Selfridge curve \begin{align*} \mathcal{C}_{k,\ell} : y^\ell = x(x+1)\cdots (x+k-1). \end{align*} Bennett and Siksek proved that i…

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

Perfect powers in sum of three fifth powers

Pranabesh Das, Pallab Kanti Dey, Angelos Koutsianas +1

In this paper we determine the perfect powers that are sums of three fifth powers in an arithmetic progression. More precisely, we completely solve the Diophantine equation $$ (x-d…

math.NT2020★ 3 cited

Repdigits in Narayana's Cows Sequence and their Consequences

Jhon J. Bravo, Pranabesh Das, Sergio Guzmán

Narayana's cows sequence satisfies the third-order linear recurrence relation $N_{n} = N_{n - 1} + N_{n - 3}$ for $n \geq 3$ with initial conditions $N_{0} = 0$ and $N_{1} = N_{2} = 1$ . In this paper, w…

math.NT2017

Perfect powers in alternating sum of consecutive cubes

Pranabesh Das, Pallab Kanti Dey, B. Maji +1

In this paper, we consider the problem about finding out perfect powers in an alternating sum of consecutive cubes. More precisely, we completely solve the Diophantine equation $(x…

math.AG2014★ 5 cited

Invitation to Integral and Rational points on curves and surfaces

Pranabesh Das, Amos Turchet

This survey article is an introduction to Diophantine Geometry at a basic undergraduate level. It focuses on Diophantine Equations and the qualitative description of their solution…