Vandita Patel

activity

20162026

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

10 citations · 19 across the 9 of their papers we have counts for

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math.NT2026

On a character-twisted analogue of Schäffer's equation

Kálmán Györy, Vandita Patel, Ákos Pintér +1

Let $f$ be a positive integer, and let $χ$ be a primitive quadratic character of conductor $f$ . Let $k$ be a positive integer, and write $B_{k} (χ, X)$ for the $k$ -th Bernoulli polynom…

math.NT2023

Power values of power sums: a survey

Nirvana Coppola, Mar Curcó-Iranzo, Maleeha Khawaja +2

Research on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) Number Theory…

math.NT2023

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

Nirvana Coppola, Mar Curcó-Iranzo, Maleeha Khawaja +2

We study the equation $(x - 4 r)^{3} + (x - 3 r)^{3} + (x - 2 r)^{3} + (x - r)^{3} + x^{3} + (x + r)^{3} + (x + 2 r)^{3} + (x + 3 r)^{3} + (x + 4 r)^{3} = y^{p}$ , which is a natural continuation of previous works carried out b…

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…