A. S. Zargar

activity

20152025

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math.NT2024

Partitions into Triples with Equal Products and Families of Elliptic Curves

Ahmed El Amine Youmbai, Arman Shamsi Zargar, Maksym Voznyy

Let $S_{l} (M, N)$ denote a set of $ℓ$ triples of positive integers having the same sum $M$ and the same product $N$ . For each $2 \leq ℓ \leq 4$ we establish a connection between a…

math.GM2024

The diophantine equation $x^{4} + y^{4} = z^{4} + w^{4}$

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 $x^{4} + y^{4} = z^{4} + w^{4}$ have…

Partitions into Triples with Equal Products and Families of Elliptic Curves

The diophantine equation x4+y4=z4+w4

The diophantine equation $x^{4} + y^{4} = z^{4} + w^{4}$