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
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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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