A Note on the Quartic Diophantine Equation A⁴+hB⁴=C⁴+hD⁴

2016/08/19 by Choudhry, Ajai
#11D25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1608.06220

Abstract

Integer solutions of the diophantine equation A⁴+hB⁴=C⁴+hD⁴ are known for all positive integer values of h < 1000. While a solution of the aforementioned diophantine equation for any arbitrary positive integer value of h is not known, Gerardin and Piezas found solutions of this equation when h is given by polynomials of degrees 5 and 2 respectively. In this paper, we present several new solutions of this equation when h is given by polynomials of degrees 2, 3 and 4.

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