most citedA Note on the Quartic Diophantine Equation

1 citations · 2 across the 4 of their papers we have counts for

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7 papers

math.GM2024

The diophantine equation

Ajai Choudhry, Arman Shamsi Zargar

Since 1772, when Euler first described two methods of obtaining two pairs of biquadrates with equal sums, several methods of solving the diophantine equation have…

math.NT2023

Expressing an integer as a sum of cubes of polynomials

Ajai Choudhry

In this paper we prove that there exist infinitely many integers which can be expressed as a sum of four cubes of polynomials with integer coefficients. We give several identities…

math.NT2023

Two pairs of biquadrates with equal sums

Ajai Choudhry

In this paper we present a new method of solving the classical diophantine equation . Two methods of solving this equation, given by Euler, yield parametric soluti…

math.NT2022

Rational quadrilaterals

Ajai Choudhry

A quadrilateral is said to be rational if its four sides, the two diagonals and the area are all expressible by rational numbers. The problem of constructing rational quadrilateral…

math.NT20221 cited

Ideal solutions of the Tarry-Escott Problem of degree seven

Ajai Choudhry

In this paper we obtain four new parametric ideal solutions of the Tarry-Escott problem of degree 7, that is, of the simultaneous diophantine equations, $\sum_{i=1}^8x_i^r=\sum_{i=…

math.NT2022

An octic diophantine equation and related families of elliptic curves

Ajai Choudhry, Arman Shamsi Zargar

We obtain two parametric solutions of the diophantine equation where is the octic form defined by $ϕ(x_1, x_2, x_3)=x_1^8+ x_…