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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## Details

### 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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## Related papers

## Cite this paper

APAIzadi, F., F. Khoshnam, & A. S. Zargar. (2014). A note on the Diophantine equations *x*_{1}* ^{k}* +

*x*

_{2}

*+*

^{k}*x*

_{3}

*+*

^{k}*x*

_{4}

*= 2*

^{k}*y*

_{1}

*+ 2*

^{k}*y*

_{2}

*,*

^{k}*k*= 3, 6. Notes on Number Theory and Discrete Mathematics, 20(5), 1-10.

Izadi, Farzali, Foad Khoshnam, and Arman Shamsi Zargar. “A Note on the Diophantine Equations *x*_{1}* ^{k}* +

*x*

_{2}

*+*

^{k}*x*

_{3}

*+*

^{k}*x*

_{4}

*= 2*

^{k}*y*

_{1}

*+ 2*

^{k}*y*

_{2}

*,*

^{k}*k*= 3, 6.” Notes on Number Theory and Discrete Mathematics 20, no. 5 (2014): 1-10.

Izadi, Farzali, Foad Khoshnam, and Arman Shamsi Zargar. “A Note on the Diophantine Equations *x*_{1}* ^{k}* +

*x*

_{2}

*+*

^{k}*x*

_{3}

*+*

^{k}*x*

_{4}

*= 2*

^{k}*y*

_{1}

*+ 2*

^{k}*y*

_{2}

*,*

^{k}*k*= 3, 6.” Notes on Number Theory and Discrete Mathematics 20.5 (2014): 1-10. Print.