A. S. Zargar

activity

20152021

collaborators

9 papers

math.NT2021

Pairs of equiperimeter and equiareal triangles whose sides are perfect squares

Ajai Choudhry, Arman Shamsi Zargar

In this paper we consider the problem of finding pairs of triangles whose sides are perfect squares of integers, and which have a common perimeter and common area. We find two such…

math.NT2020

The $\thera$-congruent numbers elliptic curves via a Fermat-type theorem

Sajad Salami, Arman Shamsi Zargar

A positive integer $N$ is called a $θ$ -congruent number if there is a $\ta$-triangle $(a, b, c)$ with rational sides for which the angle between $a$ and $b$ is equal to $θ$ and its a…

math.NT2020

Rational $θ$ -parallelogram envelopes via $θ$ -congruent elliptic curves

Sajad Salami, Arman Shamsi Zargar

We introduce a new generalization of $θ$ -congruent numbers by defining the notion of rational $θ$ -parallelogram envelope for a positive integer $n$ , where $θ \in (0, π)$ is an angle…

math.NT2019

A sextic diophantine chain and a related Mordell curve

Ajai Choudhry, Arman Shamsi Zargar

In this paper we obtain parametric as well as numerical solutions of the sextic diophantine chain $ϕ (x_{1}, y_{1}, z_{1}) = ϕ (x_{2}, y_{2}, z_{2}) = ϕ (x_{3}, y_{3}, z_{3}) = k$ where $ϕ (x, y, z)$ …

math.NT2018

Evaluation of Gaussian hypergeometric series using Huff's models of elliptic curves

Mohammad Sadek, Nermine El-Sissi, Arman Shamsi Zargar +1

A Huff curve over a field $K$ is an elliptic curve defined by the equation $a x (y^{2} - 1) = b y (x^{2} - 1)$ where $a, b \in K$ are such that $a^{2} \neq = b^{2}$ . In a similar fashion, a general Huff c…

math.NT2017

On the Diophantine equations $z^{2} = f (x)^{2} \pm g (y)^{2}$ concerning Laurent polynomials

Yong Zhang, Arman Shamsi Zargar

By the theory of elliptic curves, we study the nontrivial rational parametric solutions and rational solutions of the Diophantine equations $z^{2} = f (x)^{2} \pm g (y)^{2}$ for some simple…