Vandita Patel

activity

20172021

most citedOn perfect powers that are sums of cubes of a three term arithmetic progression

10 citations · 19 across the 5 of their papers we have counts for

collaborators

10 papers

math.NT2021

Odd values of the Ramanujan tau function

Michael Bennett, Adela Gherga, Vandita Patel +1

We prove a number of results regarding odd values of the Ramanujan $τ$ -function. For example, we prove the existence of an effectively computable positive constant $κ$ such that if…

math.NT2019

On perfect powers that are sums of cubes of a seven term arithmetic progression

Alejandro Argáez-García, Vandita Patel

We prove that the equation $(x - 3 r)^{3} + (x - 2 r)^{3} + (x - r)^{3} + x^{3} + (x + r)^{3} + (x + 2 r)^{3} + (x + 3 r)^{3} = y^{p}$ only has solutions which satisfy $x y = 0$ for $1 \leq r \leq 1 0^{6}$ and $p \geq 5$ prime…

math.NT2019

A Lucas-Lehmer approach to generalised Lebesgue-Ramanujan-Nagell equations

Vandita Patel

We describe a computationally efficient approach to resolving equations of the form $C_{1} x^{2} + C_{2} = y^{n}$ in coprime integers, for fixed values of $C_{1}$ , $C_{2}$ subject to further co…

math.NT2018

Shifted powers in Lucas-Lehmer sequences

Michael Bennett, Vandita Patel, Samir Siksek

We develop a general framework for finding all perfect powers in sequences derived by shifting non-degenerate quadratic Lucas-Lehmer binary recurrence sequences by a fixed integer.…

math.NT2018

Perfect Powers that are Sums of Squares of an Arithmetic Progression

Debanjana Kundu, Vandita Patel

In this paper, we determine all primitive solutions to the equation $(x + r)^{2} + (x + 2 r)^{2} + \dots + (x + d r)^{2} = y^{n}$ for $2 \leq d \leq 10$ and for $1 \leq r \leq 1 0^{4}$ . We make use of a fa…

math.NT2018

Perfect powers that are sums of squares in a three term arithmetic progression

Angelos Koutsianas, Vandita Patel

We determine primitive solutions to the equation $(x - r)^{2} + x^{2} + (x + r)^{2} = y^{n}$ for $1 \leq r \leq 5, 000$ , making use of a factorization argument and the Primitive Divisors Theorem…