On integer solutions of A⁵ + B³ = C⁵ + D³

Farzali Izadi and Arman Shamsi Zargar
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 5, Pages 20–24
Full paper (PDF, 154 Kb)

Details

Authors and affiliations

Farzali Izadi
Department of Pure Mathematics, Azarbaijan Shahid Madani University
Tabriz 53751-71379, Iran

Arman Shamsi Zargar
Department of Pure Mathematics, Azarbaijan Shahid Madani University
Tabriz 53751-71379, Iran

Abstract

In this note, we study the diagonal nonhomogeneous symmetric Diophantine equation of the title, and show that when a solution has been found, a series of other solutions can be derived. This shows that difference of quintics equals difference of cubics for infinitely many integers. We do so using a method involving elliptic curves, which makes it possible to naturally find any solution in a matter of minutes.

Keywords

• Diophantine equation
• Elliptic curve

AMS Classification

• 11D25
• 11G05

References

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