Pairs of equiperimeter and equiareal triangles whose sides are perfect squares

Choudhry, Ajai; Zargar, Arman Shamsi

doi:10.7169/facm/1985

Funct. Approx. Comment. Math.

2022

DOI: 10.7169/facm/1985

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Pairs of equiperimeter and equiareal triangles whose sides are perfect squares

Ajai Choudhry¹,

Arman Shamsi Zargar²

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Cited by 2 publications

References 12 publications

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An octic diophantine equation and related families of elliptic curves

Choudhry

Zargar

2023

Int. J. Number Theory

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We obtain two parametric solutions of the diophantine equation [Formula: see text] where [Formula: see text] is the octic form defined by [Formula: see text]. These parametric solutions yield infinitely many examples of two equiareal triangles whose sides are perfect squares of integers. Further, each of the two parametric solutions leads to a family of elliptic curves of rank [Formula: see text] over [Formula: see text]. We study one of the two families in some detail and determine a set of five free generators for the family.

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An octic diophantine equation and related families of elliptic curves

Choudhry

Zargar

2023

Int. J. Number Theory

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On elliptic curves assigned to a pair of right triangles with an equal hypotenuse

Zargar,

Tomita

2024

Quaestiones Mathematicae

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Pairs of equiperimeter and equiareal triangles whose sides are perfect squares

Cited by 2 publications

References 12 publications

An octic diophantine equation and related families of elliptic curves

An octic diophantine equation and related families of elliptic curves

On elliptic curves assigned to a pair of right triangles with an equal hypotenuse

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