A note on the Diophantine equations x1k + x2k + x3k + x4k = 2y1k + 2y2k , k = 3, 6

Farzali Izadi, Foad Khoshnam and Arman Shamsi Zargar
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 5, Pages 1—10
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Authors and affiliations

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

Foad Khoshnam
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

It is shown that infinitely many primitive solutions on the Diophantine equations of the title can be found on employing the theory of elliptic curves, which makes it possible to naturally find larger solutions in a matter of minutes.

Keywords

  • Diophantine equation
  • Elliptic curve

AMS Classification

  • 11D25
  • 11G05

References

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Cite this paper

APA

Izadi, F., F. Khoshnam, & A. S. Zargar. (2014). A note on the Diophantine equations x1k + x2k + x3k + x4k = 2y1k + 2y2k, k = 3, 6. Notes on Number Theory and Discrete Mathematics, 20(5), 1-10.

Chicago

Izadi, Farzali, Foad Khoshnam, and Arman Shamsi Zargar. “A Note on the Diophantine Equations x1k + x2k + x3k + x4k = 2y1k + 2y2k, k = 3, 6.” Notes on Number Theory and Discrete Mathematics 20, no. 5 (2014): 1-10.

MLA

Izadi, Farzali, Foad Khoshnam, and Arman Shamsi Zargar. “A Note on the Diophantine Equations x1k + x2k + x3k + x4k = 2y1k + 2y2k, k = 3, 6.” Notes on Number Theory and Discrete Mathematics 20.5 (2014): 1-10. Print.

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