A quartic diophantine equation inspired by Brahmagupta's identity

2020/10/16 by Choudhry, Ajai, Bluskov, Iliya, James, Alexander
#11D25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.08133

Abstract

In this paper we obtain several parametric solutions of the quartic diophantine equation (x₁⁴+x₂⁴)(y₁⁴+y₂⁴)=z₁⁴+z₂⁴. We also show how infinitely many parametric solutions of this equation may be obtained by using elliptic curves.

Related

• A Note on Quartic Diophantine equation X⁴-Y⁴=R²-S²
• Diophantine Equation X⁴+Y⁴=2(U⁴+V⁴)
• Quadratic diophantine equations with applications to quartic equations
• Diophantine Equation n(x⁴+y⁴)=z⁴+w⁴
• Is the quartic Diophantine equation A⁴+hB⁴=C⁴+hD⁴ solvable for any integer h?