1 citations · 2 across the 4 of their papers we have counts for
7 papers
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…
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…
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…
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…
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=…
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_…