A. Choudhry

collaborators

6 papers

math.NT2017

A diophantine problem on biquadrates revisited

Ajai Choudhry

In this paper we obtain a new parametric solution of the problem of finding two triads of biquadrates with equal sums and equal products.

math.NT2017

A symmetric diophantine equation involving biquadrates

Ajai Choudhry

This paper is concerned with the diophantine equation $\sum_{i = 1}^{n} a_{i} x_{i}^{4} = \sum_{i = 1}^{n} a_{i} y_{i}^{4}$ where $n \geq 3$ and $a_{i}, i = 1, 2, \dots, n$ , are arbitrary integers. While…

math.NT2017

A new method of solving quartic and higher degree diophantine equations

Ajai Choudhry

In this paper we present a new method of solving certain quartic and higher degree homogeneous polynomial diophantine equations in four variables. The method can also be extended t…

math.NT2016

A parametrised family of Mordell curves

Ajai Choudhry, Arman Shamsi Zargar

An elliptic curve defined by an equation of the type $y^{2} = x^{3} + d$ is called a Mordell curve. We obtain a parametrised family of Mordell curves whose rank, in general, is at least th…

math.NT2016

An Ancient Diophantine Equation with applications to Numerical Curios and Geometric Series

Ajai Choudhry, Jarosław Wróblewski

In this paper we examine the diophantine equation $x^{k} - y^{k} = x - y$ where $k$ is a positive integer $\geq 2$ , and consider its applications. While the complete solution of the equation…

math.NT2016

Equal Sums of Like Powers with Minimum Number of Terms

Ajai Choudhry

This paper is concerned with the diophantine system, $\sum_{i = 1}^{s_{1}} x_{i}^{r} = \sum_{i = 1}^{s_{2}} y_{i}^{r}, r = 1, 2, \dots, k,$ where $s_{1}$ and $s_{2}$ are integers such that the tota…