A Note on the Quartic Diophantine Equation $A^4+hB^4=C^4+hD^4$

Ajai Choudhry

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arXiv · 1608.06220

A Note on the Quartic Diophantine Equation $A^4+hB^4=C^4+hD^4$

Ajai Choudhry

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Abstract

Integer solutions of the diophantine equation $A^4+hB^4=C^4+hD^4$ 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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BibTeX RIS

Ajai Choudhry. 2016-08-19. A Note on the Quartic Diophantine Equation $A^4+hB^4=C^4+hD^4$. https://arxiv.org/abs/1608.06220

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