IJPAM: Volume 105, No. 4 (2015)

On Diophantine equations $X^6+6Z^3=Y^6 \pm 6W^3$

A.S. Janfada$^1$, A. Abbaspour$^2$
$^{1,2}$Department of Mathematics
Urmia University
Urmia, IRAN


Abstract. We show that the Diophantine equations $X^6+6Z^3=Y^6 \pm 6W^3$ has infinite non-trivial primitive integer solutions by rationally transferring these equation to elliptic curves with Mordel-Weil rank 1.

Received: September 1, 2015

AMS Subject Classification: 11D41, 14H52

Key Words and Phrases: Diophantine equation, elliptic curve

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DOI: 10.12732/ijpam.v105i4.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 4
Pages: 709 - 713


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