2 citations · 2 across the 9 of their papers we have counts for
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A diophantine problem concerning third order matrices
Ajai Choudhry
In this paper we find a third order unimodular matrix, none of whose entries is or , such that when each entry of the matrix is replaced by its cube, the resulting matrix i…
New solutions of the Tarry-Escott problem of degrees 2, 3 and 5
Ajai Choudhry
In this paper we obtain new parametric ideal solutions of the Tarry-Escott problem of degrees 2, 3 and 5, that is, of the diophantine systems $\sum_{i=1}^{k+1}x_i^j=\sum_{i=1}^{k+1…
Some diophantine problems concerning a pair of rational triangles with a common circumradius
Ajai Choudhry
A triangle with rational sides and rational area is called a rational triangle. In this paper we consider three problems of finding pairs of rational triangles which have a common…
A new diophantine equation involving fifth powers
Ajai Choudhry, Oliver Couto
In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation . Further, we show, using ellipti…
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…
A quartic diophantine equation inspired by Brahmagupta's identity
Ajai Choudhry, Iliya Bluskov, Alexander James
In this paper we obtain several parametric solutions of the quartic diophantine equation . We also show how infinitely many parametric solut…